Stir euronet

Introduction to trading STIRs

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Euronext refers to Euronext NV and any company which is at least a 50% owned subsidiary of Euronext NV. All proprietary rights and interest in this publicationshall be vested in Euronext and all other rights including, but without limitation, patent, registered design, copyright, trademark, service mark, connected with thispublication shall also be vested in Euronext.LIFFE CONNECT® is a trademark of LIFFE Administration and Management ("LIFFE") and is registered in Australia, HongKong, Singapore, the United States, Japan, the United Kingdom and as a European Community Trade Mark. No part of this publication may be redistributed orreproduced in any form or by any means or used to make any derivative work (such as translation, transformation, or adaptation) without written permission fromEuronext.

Euronext shall not be liable (except to the extent required by law) for the use of the information contained herein however arising in any circumstances connectedwith actual trading or otherwise. Neither Euronext, nor its servants nor agents, is responsible for any errors or omissions contained in this publication.Thispublication is for information only and does not constitute an offer, solicitation or recommendation to acquire or dispose of any investment or to engage in any othertransaction.All information, descriptions, examples and calculations contained in this publication are for guidance purposes only, and should not be treated asdefinitive.

Those wishing either to trade futures and options contracts on Exchanges within the Euronext Group, or to offer and sell them to others should establish theregulatory position in the relevant jurisdiction before doing so.

Euronext.liffe refers to the combined derivatives operations of Euronext and LIFFE. It comprises:l Euronext Amsterdam Derivative Markets, which is a regulated market under Dutch Law;l Euronext Brussels Derivatives Market, which is a regulated market under Belgian Law;l Euronext Lisbon Futures and Options Market, which is a regulated market under Portuguese Law;l LIFFE Administration and Management, which is a Recognised Investment Exchange under English Law;l MATIF and MONEP, which are regulated markets under French Law.

All are regulated markets under the European Union’s Investment Services Directive.

Euronext NVPO Box 191631000 GD AmsterdamThe NetherlandsTel +31 (0)20 550 4444.

Contents

Introduction 1

l Euronext, LIFFE and Euronext.liffe 2

Introduction to understanding Short Term Interest Rate (STIR)futures 3

l Definitions 3

The wholesale cash money markets 4

l Introduction 4

l Understanding money market risk management 4

The Inter-bank (or “Depo”) market 7

l Domestic and Eurocurrencies 8

l The importance of LIBOR and EURIBOR benchmark fixings 8

l Calculating simple interest on loans and deposits 10

l Conclusion – The inter-bank market 12

STIR futures 13

l What defines a futures contract? 13

l Why trade STIR futures contracts on Euronext.liffe 13

l What has made STIR futures so successful? 14

l What is a STIR future? 14

l STIRs as “Contracts for difference” 19

Price movements of STIR futures contracts 20

l Buying, or selling, STIR futures? 20

l The pricing mechanism of STIR futures 22

l The basis 24

l Conclusion 25

Contents continued overleaf

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Trading with STIR futures 26

l Using STIR futures contracts as a hedge 26

l Hedging where dates don’t match i.e. to non-Euronext.liffesettlement dates 28

l Trading the futures curve using ‘calendar spreads’ 31

Pricing swaps using STIR futures -Interest Rate Swaps 33

l Interest Rate Swaps 33

l The relationship between STIR futures and short dated IRS’s 34

l Using the STIR futures strip to determine the price of a one year swap rate 34

STIR options – an introduction 38

l What is an option? 38

l The advantages of buying and selling options 39

l De-coding the market jargon 40

Trading with STIR options 43

l Trading examples 43

l Exercising an option 44

l Limitations of using options – the calculation of the break-even rate 45

l Option valuation 45

One year Mid-Curve options 52

Contacts Inside back coverl l l

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In today’s financial markets, uncertainty andvolatility are ever present, especially in theinterest rate markets. Increasingly, treasurers,fund managers and others active in the world’sfinancial markets are advised to consider costeffective methods of managing their exposureto sharp moves in those financial markets.

Managing risk Treasurers, fund managers and other marketparticipants have a number of choices availableto them to help them manage their interest rateexposure. Either by using exchange-tradedproducts, like futures and options contracts, orover-the-counter (OTC) products, such asswaps, Forward Rate Agreements (FRAs), capsand floors together with the underlying cashmarkets themselves. Indeed, successful players intoday’s volatile markets will employ the full rangeof available risk management and tradingstrategies.

Exchange traded futures and options contractsoffer market participants not only a high degreeof versatility in their use, but also significantadvantages as strategic instruments, especiallywhen complemented by OTC derivative andcash market financial instruments. Indeed, whenused effectively, exchange-traded futures andoptions contracts, in conjunction with cashmarket and OTC derivative instruments canenhance returns, reduce risks and manageinterest rate risks with greater certainty,precision and economy.

Additionally, and not to be overlooked, banktreasury managers and fund managers canbenefit from less restrictive regulatoryconstraints pertaining to capital requirementswhen trading exchange-traded futures andoptions contracts.

Comprehensive portfolio Euronext.liffe offers one of the mostcomprehensive portfolios of Short Term InterestRate (STIR) futures contracts in the worldcovering the European market. Indeed,Euronext.liffe, with its flagship contract, theThree Month Euro (EURIBOR) FuturesContract, has over 99% market share in thetrading of Euro denominated STIR contracts.

Trading STIRs This brochure has been developed byEuronext.liffe in conjunction with Resource City,a leading provider of educational material tocapital market participants.The brochure hasbeen designed to provide an overview of the useand application of Short Term Interest Ratefutures and options contracts, as well as givingspecific worked trading examples.

This publication has been written to beaccessible to all levels of market participant, andas such assumes no prior financial knowledge onbehalf of the readers.Therefore, the publicationcan either be read through progressively inorder to gain an overview of today’s STIRmarket, or used selectively in order to gainspecific insights into certain aspects of the useof STIRs or the actual trading of STIRs.

This publication does not offer advice on howor whether to trade STIR futures and optionscontracts on the LIFFE market and is providedfor informational purposes only.

1Introduction to trading STIRs

Introductionl ll1

Euronext, LIFFE and Euronext.liffeEuronext was formed by the merger of theAmsterdam, Brussels and Paris cash andderivatives exchanges in September 2000.TheEuronext Group has since grown further, addingBVLP (the Portuguese cash and derivativesexchange) and LIFFE (The London InternationalFinancial Futures and Options Exchange).Thederivatives business of Euronext and LIFFE havebeen being combined under the Euronext.liffeumbrella with the migration of all of Euronext’sderivatives markets to LIFFE CONNECT®, themost sophisticated electronic derivatives tradingplatform in the world.

In this brochure:l “Euronext.liffe” refers to the combined

derivatives operations of Euronext andLIFFE, comprising the Euronext derivativesmarkets in Amsterdam, Brussels, Paris andLisbon, and the LIFFE market in London; and

l the “LIFFE market” refers to the UKRecognised Investment Exchange which isadministered by LIFFE Administration andManagement (a UK company), and whichforms part of Euronext.liffe.

For further information about Euronext.liffe’sSTIR products, please email [email protected].

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2 Introduction to trading STIRs

Introduced in 1982, the LIFFE market’s STIRcontracts have seen strong and steady growthever since, maturing into one of the leadingderivative product portfolios of any exchange.Indeed, such has been the success of thesecontracts, Euronext.liffe has captured over 99%market share of short term euro derivatives withits flagship contract, the Three Month Euro(EURIBOR) futures contract.

Please see Euronext.liffe’s Short Term InterestRate Brochure for further details onEuronext.liffe’s STIR product portfolio.

DefinitionsIn order to understand STIRs fully, it is importantto understand some initial definitions, specifically,what a derivative is and from where it derives.

l Definition of a derivativeAs the name suggests, a derivative product isthe term applied to any product that derivesfrom another product, usually (but notalways) the underlying cash markets.

STIRs, as derivative products, derive from theunderlying cash money markets, which will beexamined in more detail shortly.

It is also appropriate at this point, to define whata futures contract is:

l Definition of a futures contractA futures contract is a legally bindingagreement, concerned with the buying, orselling, of a standardised product, at a fixedprice, for cash settlement (or physicaldelivery1) on a given future date

In the case of STIR futures, the “standardisedproduct” is short-term interest rates, (whichwill also be expanded on further in the futuressection of this text).

Therefore, having defined STIRs as both“derivatives” of the underlying cash moneymarkets, and more specifically “futurescontracts” on short-term interest rates, we cannow turn our attention to understanding what amoney market product actually is.This will aidyour understanding of STIR futures contractsand help put them into context.

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Introduction to understanding Short Term Interest Rate(STIR) futures

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1 STIR contracts are all cash-settled, there is no physical delivery, unlike the bond futures contracts.

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IntroductionEach country’s own domestic money market isan “OTC” (over-the-counter2) wholesale market,trading in two main areas:

1. Unsecured cash – the so-called “inter-bank”, or “Depo”, market (we willfocus more closely on the “depo” market inthe next section, as it is closely related tothe STIR market), and;

2. Secured cash – the so-called cash-basedsecurities, or “tradeable paper” market e.g.Treasury Bills, Certificates of Deposit (CDs),Commercial Paper (CP), Bankersacceptances (BAs), Floating Rate Notes(FRNs) and of increasing importance, theso-called “repo” (sale and repurchaseagreement) market.

All of the above OTC deals are done largely overthe telephone (either directly between the twocounterparties concerned, or via moneybrokers) or, increasingly, via computerisedelectronic broking systems.

Collectively these markets are referred to as the“cash” markets, because real sums of moneywill actually be debited and credited torespective accounts. However, the mostimportant thing to remember about them is that,because they trade OTC (rather than trading asa standardised contract, on a regulated exchange,such as the LIFFE market), there is realcounterparty risk to consider.

“Counterparty risk” refers to the risk thateither counterparty could actually default on thedeal and thereby leave the other counterpartyexposed.

The main market “players” in these wholesalecash money markets are: International andDomestic Banks, Building Societies (UK),

Investment Houses, Fund Managers, large/mediumsized Corporations and Governments3.

A “Wholesale” market is distinct from a “Retail”market, in that the wholesale markets are usuallyconcerned with transactions for large sums ofmoney, i.e. in excess of say £500,000 (or theforeign currency equivalent).Whereas “Retail”generally refers to the day-to-day transactionsof the general public, in the form of deposits,personal loans, mortgages etc.

Although there is no official definition of whatconstitutes a “money market” product:

The majority of all financial instruments tradedin the money markets will have ‘a maturity’of one year, or less.

Although some money market instruments canhave longer maturities, (CDs for example canhave maturities of up to 5 years), this length ofterm is normally the area where the so-called“Capital Markets”, which specialise in mediumand long term transactions, take over.

Understanding money market riskmanagement All money market products are concerned withtwo of the three main types of risk:

l Interest rate risk; andl Counterparty (or credit) risk.

(The third main type of risk is Foreign Exchange(FX), or Currency Risk.)

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2 An over-the-counter or OTC market is where the two counterparties concerned strike a deal where all aspects arenegotiable.The two parties will therefore agree such things as currency, amount, period and price.

3 Only tradeable paper, not Inter-bank, as Governments will not deal “unsecured”.

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Interest rate risk What can interest rates do? Well, they can go up,go down, or stay the same. Nobody knows forcertain what is going to happen next, which iswhy this risk has to be managed.

The level of interest rates in any domesticmarket is determined by numerous factors.For example, supply and demand, governmentmonetary policy4, the current economic climate,the strength or weakness of the currency etc.The markets can be volatile and therefore, alterquite frequently.Any action taken based uponactual, or possible, interest rate movement isknown as managing interest rate risk.Themanagement of interest rate risk in the short-term cash money markets is dependent uponwhether one is a borrower, or a lender, of funds.

The borrowerIf you are a borrower of funds (i.e. createliabilities), then your risk is that if interest ratessubsequently come down, you could have waitedand borrowed at a lower (ie cheaper) rate!

For example, assume that a dealer borrowsmoney at say, 5% for a three-month period.Then,the following day, interest rates for the three-month period move down to say, 4.75%. If thedealer had waited one more day, he could haveborrowed at this lower rate, ie paid less intereston the loan.

Therefore, a borrower of funds always wantsto borrow as cheaply as possible. (In bankingterminology, borrowing funds is also known ascreating a liability, ie you are liable to pay themoney back).

The lenderIf you are a lender of funds, (ie create assets),then your risk is that if interest ratessubsequently go up, you could have waited andlent at a higher (ie more expensive) rate.

For example, assume that a dealer lends moneyat say, 5% for a three-month period.Then, thefollowing day, interest rates for the three-monthperiod move up to say, 5.25%. If the dealer hadwaited one more day, he could have lent at thishigher rate, ie received more interest on the loan.

Therefore, as a lender, one always wants tolend as expensively as possible. (In bankingterminology, lending funds is also known as‘creating an asset’, ie it is your assets that youare lending).

Counterparty, or credit risk However, a lender of funds in the cash moneymarkets also incurs another major risk –counterparty, or credit risk.This is the risk thatthe funds that have been lent, will not be re-paidby the borrower. It is for this reason that allbanks (and other financial institutions thatparticipate in the wholesale money markets),have very strict lending guidelines set in place.

These include:l to whom they can lend money;l the amount they can lend; andl the period of the loan.

These guidelines are normally known as “creditlimits”. Such limits will be set up by a bank’scredit department, whose sole purpose it isto assess and monitor the ability of existing(and potential) counterparties, to repay moneyborrowed from the bank.

Money market products as “On balancesheet” transactions A bank will account for all such transactionsmentioned above, on what is known as itsbalance sheet, which is split into assets andliabilities.


4 Monetary policy in the Euro-in region is managed by the ECB (European Central Bank), rather than being the responsibility ofeach individual government.

Operations such as cash loans (assets) anddeposits (liabilities) that actually involve aphysical payment (and consequent risk) aretherefore termed “On-balance sheet” exposures.

Having “On balance sheet” exposures dictatesthat a Bank is required, by the Bank forInternational Settlements (BIS), via its CapitalAdequacy Directive (CAD), and local regulatoryauthorities, to set aside, for no return, aproportion of its capital, in case of non-repayment and doubtful debts.

This is an important aspect of all money markettrading, as it can make “On balance sheet”trading expensive to conduct.

This major drawback is one of the main reasonswhy the use of STIR futures (which are termed“Off balance sheet,”) have grown rapidly as analternative and more cost effective, interest raterisk management tool.

In the section “STIR Futures”, the reason as towhy STIR Futures are termed as “Off balancesheet” products and the benefits thereof will beexplained in detail.


The significance of the so-called “inter-bank” or“Depo” market is that it is the underlying cashmarket from which STIR futures derive.

It is therefore necessary to look at the inter-bankmarket in greater detail.The inter-bank market(in market jargon terms, often referred to as the“Deposit” or ‘Depo’ market), is a wholesale OTCmarket. It is the part of the money markets thatis concerned with the borrowing, or lending, oflarge sums of cash (ie at least £500,000 or foreigncurrency equivalent), totally unsecured, forcertain fixed periods of time.

As the name suggests, the interest rates quotedare known as “inter-bank” rates, simply becausethey represent the best rates at which the majorbanks, and other large financial institutions (butnot Governments5), are prepared to deal.All currencies that trade in the internationalmoney markets have an inter-bank cash market:

ExampleA typical set of rates, as given below, illustratesthe Sterling (GBP) inter-bank cash ratesapplicable, for the various periods concerned:

Figure 1: Sterling inter-bank rates

Period Offer Bid

O/N 4.70 4.60

T/N 4.65 4.55

1 wk 5.00 4.75

2 wk 5.00 4.75

1 mth 5.00 4.75

2 mth 5.00 4.75

3 mth 5.00* 4.75

6 mth 5.25 5.00

9mth 5.50 5.25

12mth 5.75 5.50

* the significance of the three-month offered rate will beexplained shortly

Trading periodsFigure 1 (above) illustrates Sterling (£) inter-bankcash rates for certain fixed periods of time. Forillustration purposes, assume that it is publishedby a London bank that is active in the sterlinginter-bank cash market.The fixed periods aremarked in bold.

O/N: “Overnight” ie cash lent/borrowed fora one-day period, from today untiltomorrow6

T/N: “Tom/Next” ie cash lent/borrowed for aone-day period, but from tomorrow untilthe next day7

1 wk “One week” ie cash lent/borrowed for a7-day period

2 wk “Two weeks” ie cash lent/borrowed fora 14-day period

1 mth “One month” ie cash lent/borrowed forone calendar month

2 mth etc.

You will note that there are two interest ratesquoted for each period.This style of quote isknown as a “two-way” price, representing theinterest rates at which a market maker (ie thebank making the price) is prepared to lend, orborrow, money in the inter-bank market.

The highest rate in an inter-bank two-way quote,is always the rate at which a market-maker (bank)would be prepared to lend cash for the periodconcerned.This rate is known as the “offer”.

Similarly:

The lowest rate in an Inter-bank two-way quote,is always the rate at which a market-maker (bank)would be prepared to borrow cash for theperiod concerned.This rate is known as the “bid.”


The Inter-bank (or “Depo”) market l ll

5 Governments do not normally deal “unsecured”.6 If today was a Friday, then “Overnight” would actually mean from today until Monday ie a three-day period.7 Similarly, if today was a Friday, then “Tom/Next” would mean from Monday until Tuesday.The markets do not trade on weekends, or

Bank Holidays.

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A market-maker’s offer is naturally at a higherrate of interest than his bid, as lending high andborrowing low is how a market-maker in theinter-bank market expects to make a profit!

Example:Assume a market-maker quotes the three-monthInter-bank price on the rates given above.Thismeans he would be willing to:

l LEND cash (unsecured) for three monthsat 5%, (LIBOR)8 ie his offer, and,

l BORROW cash (unsecured) at 4.75%,ie his bid.

The difference between the market-maker’s offerand his bid, is known as the “dealing spread”.

Note: Since this is an inter-bank market, anyother non-bank participants, e.g. largeCorporates, may well have to pay a “marginover” to borrow funds. For example, for threemonths say 5.00% plus 1⁄4 % margin = 5.25%.The size of the margin added to the offered rate,for non-bank players, depends on the creditworthiness of the institution concerned.Similarly, a Corporate wishing to place money ondeposit may only be quoted, say 4.50% (ie bidside minus 1⁄4 %).

Domestic and EurocurrenciesThe inter-bank markets for the variouscurrencies that trade in the international moneymarkets come in two forms:

l DomesticThe definition of a domestic currency is onethat is held in its country of origin.

For example, sterling (GBP) is the domesticcurrency of the UK money markets.Whereas,the euro is the domestic currency of the(currently) 12 countries which collectively makeup the eurozone (ie Germany, France, Italy,Austria, Spain, Portugal, Belgium, Netherlands,Luxembourg, Finland, Ireland and Greece).

l Eurocurrencies The definition of a eurocurrency is anycurrency that is held outside its country oforigin.

For example, USD deposits traded in the UKmoney markets are known as “eurodollar”deposits, Similarly, sterling traded outside of theUK would be referred to as “eurosterling” etc.

It is therefore very important not to confuse theterm “eurocurrency” with the term “euro.”

The “euro” is the name given to the unit ofcurrency created in January 1999 by theEuropean Central Bank.Whereas,“eurocurrency” is the generic term given to anycurrency that is held (or being traded) outsideits country of origin.

Technically therefore, the euro would not betermed a eurocurrency, unless it is being tradedoutside the euro zone.

The importance of LIBOR and EURIBORbenchmark fixings

LIBOR Referring to the Sterling Inter-bank rate sheetillustrated (Figure 1), you will note that there isan asterisk* by the three-month offered rate,which is also printed in bold.This is to alert youto the importance of this rate, with regard theSTIR futures markets. In order to understand theconcept of STIR futures, it is important tounderstand the significance of this three-monthoffered rate.

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8 The concept of LIBOR will be covered shortly.

At 11am each day, in London, an “official fixing”of a whole range of “LIBOR” rates, for a varietyof currencies, takes place under British BankersAssociation (BBA) rules, for any currency “fixing”in London. For example, for the major currencies“fixing” in London, the BBA will publish anovernight, one week and two week fixing as wellas 12 monthly fixings out to one year.

LIBOR stands for “London Inter-bankOffered Rate”.

The fixings are determined as follows:

At just before 11am, a group of 16 London bankssubmit their offered rates for a variety of the Inter-bank periods mentioned above, in order to allowan official “fixing” of this period to take place.

For example, when setting the official three-month Sterling (or currency code GBP, orsymbol £) LIBOR rate, the four highest and thefour lowest rates submitted are discarded.Subsequently, the official three-month GBPLIBOR rate is then ‘fixed’ at 11am, by establishingthe mean average of the remaining eight banks’offered quotes.

It is this official three-month LIBOR (orEURIBOR – see below) “fixing” that is themost significant to us here, as this is also the“underlying product” that the STIR futurescontracts are based on.

For example, when someone trades a STIRfutures contract, they are trading what they thinkthis official three month LIBOR (or EURIBOR –see below) fixing rate will be for the currencyconcerned, on a given future date. (However, thisdoes not mean that the “offered side” of thethree-month inter-bank rate will remain at thislevel for the rest of the day’s trading. Rather, thisofficial fixing rate at 11am is merely used as a“reference rate” or “benchmark”, against whichthe pricing, or settlement, of a variety of LIBOR-

based financial transactions (such as STIR futurescontracts), can be made).

It is important to realise therefore, that theword ‘LIBOR’ actually refers to the fixing of anycurrencies traded in London and agreeing toabide by a BBA LIBOR fixing.

It is also possible to have an official USD LIBORfixing (ie US Dollar inter-bank rates “fixed” inLondon), or a CHF LIBOR fixing (ie Swiss francrates “fixed” in London). Similarly, it is possible tohave a Yen LIBOR fixing (ie Yen rates fixed inLondon), or even a “euro-LIBOR” fixing (ie eurorates fixed in London – see notes below on“EURIBOR”).

The importance of the three monthLIBOR rate It is the three month fixing that has mostsignificance for the STIR market, as this isessentially the “underlying cash product” that theSTIR futures contracts derive from.

For example with regard to Euronext.liffe’s STIRfutures contracts, LIBOR is the reference rateused for the Three Month Sterling (Short Sterling)Interest Rate futures contract (£ LIBOR), and theThree Month Euro Swiss Franc (Euroswiss)Interest Rate futures contract (CHF LIBOR).

Other countries have their own official interestrate fixings for domestic and eurocurrencies, andthese are used in similar circumstances, forexample:

l SIBOR: Singapore Inter-bank Offered Ratel TIBOR:Tokyo Inter-bank Offered Rate9


9 With reference to the STIR contracts, the yen denominated futures contract is settled against the TIBOR fixing.

EURIBOR The initial struggle for supremacy concerninga “euro reference rate” needs to be mentionedhere.When the euro was first introduced asa single currency, in January 1999, it was assumedthat the main “fixing” centre would be inLondon, ie a LIBOR rate for the euro (the “euro-LIBOR rate” as mentioned above). However, thishas not been the case.

For a variety of reasons, the main centre for thefixing of euro benchmark interest rates has nowestablished itself in Brussels, where a panel of 49banks, calculate their own official benchmarkinterest rates for the euro.The majority of thepanel are from Euro-in countries, but alsoinclude, for example, the UK, which is a memberof the European Union, but is not a participant inthe euro itself.

This reference rate is known as the EuropeanBankers Federation (EBF) “EURIBOR” rate.

Strictly speaking it should be referred to as the‘euro-EURIBOR rate’, but because the euro isthe only currency being fixed under this newEBF benchmark reference rate, it is only everreferred to as the “EURIBOR” rate.

EURIBOR stands for “Euro Inter-bankOffered Rate”.

Calculating simple interest on loansand depositsIn order to fully understand where “minimumtick size movements” on Euronext.liffe’s STIRfutures contracts come from, it is important tounderstand the calculation of interest paid, orreceived, in the inter-bank markets.The amountof interest to be paid, or received, on a loan ordeposit, is calculated at the start of the fixedperiod to which it relates, but is paid at the end(known as “in arrears”). It is calculated using thefollowing simple interest formula:

Simple interest =

Principal Amount x % Rate x

Using the data in Figure 1, on a market-maker’sthree month quote of “5.25 – 5.00” for the threemonth period, on a principal amount of say£500,000, the amount of interest to be paid(or received), at the end of the period (ie atmaturity), can be calculated as follows:

*See notes below on Value Dates & Day Basis.

Hence, in a) above, as a market user:If you were a borrower of funds and dealt atthe market maker’s offer of 5.001%, you wouldborrow (“go long”) £500,000 at the outset.You would also repay the principal plus interest(ie £500,000.00 + £6,232.88) at the end of thefixed period (in this case 91 days later).

In b) above, as a market user:If you were a lender of funds and dealt at themarket maker’s bid of 4.75%, you would lend(“go short”) £500,000 at the outset.You wouldalso receive principal plus interest (ie £500,000 +£5,921.23) at the end of the fixed period (in thiscase also 91 days later).

A dealer making a two-way price and dealing onboth sides simultaneously would therefore makea profit of £311.64.

Actual No.of days in period

Actual No.of days in year

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Value dates & day basis Sterling (GBP), as the UK’s Domestic currency,normally deals ‘value today’, ie out of today,calculating the Actual number of days in thedeposit period and dividing by a 365 day basis(known as Bond basis).This would be writtenas “Actual/365”.

Whereas:

Most eurocurrencies deal ‘value spot’ (ie twobusiness days forward), calculating the Actualnumber of days in the deposit period, butdividing by a 360 day basis (known as MoneyMarket basis).This would be written as“Actual/360”.

Example actual/365 (£)If today is Monday, 9th May, 2005, then acalculation for a Sterling deposit, for say athree month period, would have a value date of6th May ie the same day on which the tradewas enacted.

This is referred to as “T (trade) + 0 (no days)”and an end date, or maturity date, of 9th August(ie same date, but exactly three calendar monthslater, providing it is a good business day). Hencein this case, the trade date and value date are thesame, and Sterling is said to trade “out of today”or “value today”.

The actual number of days in the deposit periodwould then be calculated (in this case 9th May –9th August, 2005 = 92 days) and would then bedivided by the Day Basis applicable to Sterling ie365 days.

However, this is not the case witheurocurrencies (ie euros, Swiss Francs,Yen etc.trading in London).

Example actual/360 (€,CHF,Yen)If one were doing the same calculation as givenabove, but for say euros, then the value datewould be two business days forward from thetrade date of Monday, 9th May.

This would be referred to as “T (trade) + 2 (twobusiness days forward)”, ie out of Wednesday11th May, (also known as “out of spot”) and withan end date, or maturity date, of 11th August (iesame date but exactly three calendar monthslater, providing it is a good business day). Hence,in this case the trade date (9th May) and thevalue date (11th May) are clearly not the same!

This is because most eurocurrencies trade “outof spot”, not “out of today”.

The actual number of days in the deposit periodwould then be calculated (in this case 11th May –11th August 2005 = 92 days) and would then bedivided by the Day Basis applicable to euros ie360 days.

The actual number of days in a depositperiod It is important to realise that, in the inter-bankmarkets, the actual number of days in any givendeposit period can vary, according to the actualdates in question.

Hence a three month run will not always beexactly a quarter of a year ie 91, or 90 days,but is normally somewhere between say 89 – 93days. Shorter, or longer, periods are likely tooccur where a weekend, or Bank holiday periodis concerned.This is because the start date(value date) and end date (maturity date) canonly be on ‘good’ business days.

For example, assume a Sterling three monthtransaction where the actual dates are 2nd Feb –2nd May 2005. Using a calendar, you will see that2nd Feb is a Wednesday. However, 2nd May was aBank Holiday in the UK, therefore standardmarket practice is to go forward to the nextgood business day ie Tuesday 3rd. (The onlyexception to this would be if, by going forward, it


put you into the next calendar month. In thatcase you would go backwards, to the previousgood business day).The actual number of dayswould therefore be 2nd Feb – 3rd May = 90days.

By contrast, a euro three month transactionwhere the actual dates are say 5th April – 5thJuly, 2005, would give rise to an actual numberof days of 91 days.

Using the correct day base Having established the actual number of days,one must also remember that the Day Base canvary, according to the currency being used.Hence, in the Sterling example given above, the93 (Actual) days, would then be divided by theSterling Day Base of 365.Whereas, with the eurocalculation, this would be 91 (Actual) days,divided by the euro Day Base of 360.

Hence in summary, with regard the currenciesthat have a Euronext.liffe STIR futures contractbased upon them:

Currency Value Date Day Basis

Sterling Same as Trade date, hence 365

“T + 0”

€, CHF,Yen Trade date + two business 360

days, hence “T + 2”

Conclusion – The inter-bank marketThe inter-bank market is the most basic of allmoney market products. It is concerned with theborrowing or lending of cash, totally unsecured,for fixed periods of time. Moreover, becausemoney actually changes hands, there is realcounterparty risk to consider.

Banks, and other financial institutions, that deal inthe Wholesale Cash Money Markets, therebycreate what are known as “On Balance Sheet”exposures, having to set aside a proportion oftheir exposure, as provision for bad and doubtfuldebt.This makes On Balance Sheet transactionsexpensive to conduct.

The main users of the inter-bank markets, aretherefore those with a physical cash requirement.For example, Banks, Building Societies (UK), FundManagers or large Corporations, who findthemselves with excess funds, either overnight(O/N) or for a “fixed” term (ie up to 12 months),or in need of such funds.

They can use the wholesale cash money markets,in order to gain access to other participants, andso match their funding requirements.

However, those with a desire only to manageinterest rate risk (ie without a physical cashrequirement) can access a more prudent andcost effective route: Futures!

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What defines a futures contract?Unlike the OTC Inter-bank markets, from whichthey derive, all of Euronext.liffe’s STIR futurescontracts are traded electronically (via LIFFECONNECT®) on a regulated exchange.

STIR future contracts are defined as:A legally binding agreement, concerned with thebuying, or selling, of a standardised amount of agiven short term interest rate product, at a fixedprice, for cash settlement on a given future date.

STIR futures contracts derive from the cashinter-bank markets, previously mentioned, sincethey are concerned with the trading of theimplied value of three month LIBOR (£ andCHF) EURIBOR (€) or TIBOR (Yen), but froma given future date.

Why trade STIR futures contracts onEuronext.liffe?Trading interest rate risk using Euronext.liffe’sSTIRs has many advantages, including:

l LiquidityExchange traded futures (and options) arestandardised contracts.They provide auniformity of specification and quality, whichenhances market liquidity and efficiency. Intheory, it is possible to have a futurescontract on any product, but strong userdemand is what produces liquidity.

“Liquidity” refers to the depth of themarket, ie a large number of buyersand sellers creating substance to themarketplace, allowing for a free flowof transactions at any given price.

Liquidity is therefore the essential factor forthe survival of any futures contract.Euronext.liffe is dominant in STIR futurescontracts, as well as having strong bond,swap and equity product portfolios, with itsbiggest, and most liquid contract, being theThree Month Euro (EURIBOR) Interest Ratefutures contract.

l Central MarketplaceWith exchange traded futures (and options),buyers and sellers enjoy immediate access toa central marketplace, where a large numberof competing buyers and sellers can transacttheir business, via the LIFFE CONNECT®

electronic trading system.

l Price transparencyEuronext.liffe’s electronic trading platform,LIFFE CONNECT®, provides continuous andcompetitive price discovery and globaldissemination of price information. Inessence “price discovery” means that thebest bid and best offer in any given contract,is always displayed on the trading screen and“global dissemination of price information”means that computer terminals aredistributed to a world-wide audience!

Together, these two aspects make it possiblefor traders (no matter how big, or howsmall) to compete on equal terms andfacilitate the timing of trading decisions, asquickly and accurately as possible.

l Central ClearingUnlike the OTC markets, the LIFFE market’sfutures and options contracts benefit from acentral clearing counterparty, known asLCH.Clearnet.This means that counterpartyrisk is considerably reduced.

Upon matching and registration of purchasesand sales, LCH.Clearnet, (which isindependent of the Exchange), becomes theeffective buyer to every seller, and seller toevery buyer. Hence LCH.Clearnet becomesthe guarantor of all futures (and options)trades to so-called Clearing Member firms.

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STIR futures l ll5

LCH.Clearnet thereby ensures the integrityof the Exchange’s contracts, by calling onMember Firms, for so-called Initial Margin (iefunds placed with LCH.Clearnet at the timethat a new position is taken), and Variationmargin (ie additional funds placed with orwithdrawn from LCH.Clearnet, where aposition is showing an open loss or gain), onall positions. For further details on themargining system used by the LIFFE market,London SPAN® version 4, please seewww.euronext.com.

l Regulated marketThe LIFFE market is a RecognisedInvestment Exchange (RIE) under the UKFinancial Services Act.As such the LIFFEmarket is required to ensure that all businessis conducted in an orderly manner and thatthe Exchange affords proper protection toinvestors.

What has made STIR futures so successful?STIR futures contracts have been so successfuland have expanded so rapidly, simply becausethey offer something that the underlying OTCcash markets alone cannot offer. Chiefly thereare three reasons:

1. They enable traders to trade for a futurevalue date, thereby allowing them theopportunity to hedge (ie cover, or protect) aforward interest rate exposure and henceremove some of the uncertainty associatedwith interest rate risk management.(Speculators on the other hand, are on theother side of the fence.They are instrumentalin providing the liquidity that is needed forfutures exchanges to succeed, by speculating(ie taking risk) on future price movements!)

2. They are termed ‘Off-Balance Sheet’products.They do not involve the physicalrisk of the underlying transaction amount(unlike the Cash Money Markets), but are inthe main based on ‘contract for difference’

settlement. By trading STIR futures, a traderwill utilise less of a Bank’s capital10 thanwould be the case with ‘On-Balance Sheet’transactions, such as ‘cash’.

3. Counterparty risk is standardised inthe Futures markets.This is due to thecombination of the margining system uniqueto the Futures Exchange and the role of theclearing house (LCH), standing ascounterparty to every trade. Consequently,‘counterparty risk’ (which is prevalent in thecash markets) is all but eliminated.

What is a STIR future?STIRS are short-term interest rate derivatives,that derive from the underlying three-monthLIBOR,TIBOR or EURIBOR rate traded in theOTC Cash Money Markets.

The Short Term Interest Rate (STIR) FuturesContracts currently traded on Euronext.liffe, areas follows:

Contract Underlying product

Three Month Euroyen

(TIBOR) Interest Rate

Three month Yen

TIBOR fixing rate

Three Month Euro

Swiss Franc (Euroswiss)

Interest Rate futures

contract

Three month CHF

LIBOR fixing rate

Three Month Sterling

(Short Sterling) Interest

Rate futures contract

Three month £ LIBOR

fixing rate

Three Month Euro

(EURIBOR) Interest

Rate futures contract

Three month €

EURIBOR fixing rate

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10 In fact, Futures do NOT require credit risk weighting for BIS capital adequacy purposes.

Contract monthsThe STIR futures contracts are standardisedcontracts that trade for specific so-called“quarterly” contract months.These are:

March, June, Sep, Dec.

Moreover, the STIR contracts actually expire (iestop trading) on the third Wednesday ofthe contract month in question at11.00 a.m. (London or Brussels time dependingon the contract). In practice, this means thatShort Sterling stops trading at 11.00 am (Londontime) on the third Wednesday (ie Sterling trades“out of today”).

However, the Three Month Euro (EURIBOR) andThree Month Euro Swiss Franc (Euroswiss)futures contracts actually stop trading at 11amBrussels time on two business days prior to thethird Wednesday.This is because they trade ‘outof spot’ (ie two working days hence.) This hasgot nothing to do with whether they are fixedagainst LIBOR, or not – it is just that they are allclassified as “eurocurrencies”. For example, theEuroswiss contract trades “out of spot”, but hasa LIBOR fixing.

Traders of STIRs, are therefore tradingwhat they think the official three-monthCash Inter-bank LIBOR (Sterling,Euroswiss), or EURIBOR (Euro) or Tibor(Euroyen TIBOR) fixing rate will be on agiven future date.

For example, September ’05 EURIBORFuture:What do I think the official three monthEURIBOR (Brussels) fixing rate will be at11.00am (Brussels time) on the Mondaypreceding the third Wednesday ofSeptember 2005?

Or, Dec ’05 Short Sterling:What do I think the official three month LIBOR(London) fixing rate will be at 11.00am (Londontime) on the third Wednesday of December 2005?

However, this does not mean that a trader has tokeep a position until expiry. STIR futures aretradeable, which means they can be bought andsold on an on-going basis, right up until the dayand time of expiry, at which time the contractwill cease to exist!

What is meant by the serial months? In order to widen the menu of contractsavailable for trading, so-called “serial months”have also been introduced, such that the frontthree calendar months are always available fortrading.

A “serial month” therefore simply refers to acontract month other than the standardquarterly futures date mentioned above.

For example:If it is now 1st June, 2005, then the EURIBORcontract months available for trading would beas follows:

l June (Quarterly) ‘front’ month(expires Monday preceding 3rd Wednesday.of June)

l July (Serial month)l August (Serial month)l Then Sept (Quarterly) and subsequent

quarterly months.

However, all other aspects of serial monthtrading are the same.

For example:If you traded the July ’05 EURIBOR (serialmonth) contract you would be trading:

What do I think the official three monthEURIBOR (Brussels) fixing rate will be at 11am(Brussels time) on the Monday preceding thethird Wednesday of July 2005?


Hence it is still a three month EURIBOR-basedcontract, but for a different calendar month!

What are the standard contract sizes onEuronext.liffe? Unlike the OTC Cash Money Markets, where thesize of each trade has to be agreed between thetwo counterparties concerned, each STIR futures“contract” is based on a nominal standardcontract size, as determined by the Exchange.

For example:One Short Sterling contract is worth a nominal£500,000.

Therefore, if you were to trade in 20 contracts,you would be trading a nominal11 value of:

£500,000 x 20 = £10,000,000 worth of shortterm interest rate movement.

The contract sizes for all the STIR contractstraded on LIFFE are as follows:

Contract Unit of trading (Nominal contract size)

Three Month Euro (EURIBOR)

Interest Rate futures contract €1,000,000

Three Month Sterling (Short

Sterling) Interest Rate futures

contract £500,000

Three Month Euro Swiss Franc

(Euroswiss) Interest Rate futures

contract CHF 1,000,000

Three Month Euroyen (TIBOR)

Interest Rate futures contract ¥100,000,000

Why are futures contracts known ascontracts for difference? Futures are known as ‘contracts for difference’,simply because the underlying “nominal” valueof the contract is not pledged.

For example, a dealer trading in say, theEURIBOR futures contract, is not risking acapital sum of €1,000,000. Rather, the nominalcontract size is merely used to calculate theminimum tick size movement that each futurescontract represents (see minimum tick sizemovement calculations below).

This is what is then used to calculate the profit,or loss, thereby generated on any giventransaction.This is an important point, becauseit means that STIR futures are therefore termed“Off Balance Sheet” transactions.

Why are STIR futures termed“Off balance sheet”? One of the most important aspects of tradingSTIRs is that (unlike the inter-bank market), theyare termed “Off Balance Sheet” products.

STIR futures are termed “Off Balance Sheet”,because they do not involve the physicalborrowing, or lending, of the nominal underlyingcontract value. Moreover, since the nominalcapital sum is never at risk, a Bank, or otherfinancial institution, can trade more of them(as opposed to trading in the Inter-bank market),without “inflating” the Balance Sheet.

Because they are classified as “Off BalanceSheet” instruments, the Capital Adequacyrequirement for STIR futures contracts, is alsogreatly reduced.

In essence, this means that STIRs are a morecost effective tool for managing interest raterisk, than the underlying inter-bank markets, fromwhich they derive.


11 Trading a ‘nominal’ value in the STIR Futures markets is distinct from the Cash markets, where the actual underlying cash sumis physically borrowed, or lent.

As you will see shortly, the nominal contractvalue is never at risk, but is merely used todetermine two important aspects of dealing a)the total number of contracts required and b)the calculation of the “minimum tick size value”for each contract.

How are the minimum tick sizemovements on STIRs determined? The tick size values for each of the STIR futurescontracts are based on the simple interestformula used for calculating interest in theInter-bank market.

The minimum tick size movement variesaccording to the contract concerned, but formost contracts is referred to as “a 01”.

The value of a “01” actually means a one basispoint move, in interest rate terms, from say 4%(ie 96.00 futures equivalent price) to 3.99%(96.01 futures equivalent price).

In order to understand how the futures marketcalculates the value of “an 01”, it is thereforeimportant to re-visit the way in which thecalculation of interest is determined in theinter-bank market, from which STIR futuresare derived.

You will recall that in the inter-bank market,interest is calculated “in arrears”, using theSimple Interest formula:

Simple interest =Principal Amount x % Rate x

Let us now assume that a bank dealer is able toborrow euro in the inter-bank market at say3.99%, for a three month period (say 90 days,using actual number of days). Similarly, let usassume that he can also lend the same amount,at a higher rate of interest, say, 4.00% (ie adifference of “.01”) for a similar period.Borrowing cheaply and lending expensively ishow a dealer hopes to make a profit.

On a principal amount of say, €1,000,000, it isnow possible to calculate the amount of interestto be paid, or received, at the end of the fixedperiod, ie at maturity. In this case, the differencebetween the two amounts should represent thedealer’s profit on the transaction.

*See notes on value dates and day basis

The difference between the two amountsrepresents the dealer’s profit. Hence in thisexample, a dealer in the inter-bank market,borrowing euros at 3.99% and lending at thehigher rate of 4.00%, would make a profit ofonly €25.00.

However, since the inter-bank market is“On Balance Sheet”, a certain amount of capitalwould also have to be set aside, for bad anddoubtful debt.This means that, in practice, it ismore expensive to transact, when comparedwith using “Off Balance Sheet” products, such asSTIR interest rate futures. For example, in theabove scenario, the cost of capital could morethan wipe out this tiny profit.

The STIR futures market, was therefore devisedas an alternative “Off Balance Sheet” market, fortrading interest rate risk, without the underlyingcapital sum involved actually being pledged.

STIR futures contracts are considered “OffBalance Sheet” because all transactions arebased on a “nominal” contract size, which canthen be used to determine a nominal “tick size”movement.This means that no actual capital sum

Actual No.of days in period

Actual No.of days in year


changes hands and therefore cannot be at risk.To demonstrate how the STIR futures marketworks, now let us assume that the bank dealerdoes not wish to borrow or lend, but simplywishes to take a view on interest rates, and assuch, trades one Three Month Euro (EURIBOR)Interest Rate futures contract.

Let us assume that he deals simultaneously at3.99% equivalent (ie futures price of 96.01) andat 4.00% equivalent (ie futures price of 96.00) tolock in a difference of “one tick” or a “01”ie 0.01/100.We will further assume that ratherthan an actual sum, a nominal €1,000,000contract value is now applied.

To further simplify things, with STIR futurescontracts, the period of time is also standardised,in that it is no longer calculated based on theactual number of days in a given three monthperiod, but is simply expressed as:

“1/4 of a year”

(Since no actual physical borrowing or lending isgoing to occur, this is not a problem!)

Hence the calculation has now beenreduced to:

Therefore the value of each “01” or one tickis €25.00.

Hence a one tick move (up or down) in theEURIBOR futures contract, is equivalent to“.01%” interest rate movement in the underlyingmarket, but because no capital sum ever changeshands, it is reduced to a tick value of €25.00profit, or loss, per contract.

Note:The Three Month Euro (EURIBOR)Interest Rate futures contract actually trades inhalf ticks (.005) as well as full ticks (.01) ie if the

price moves from say 96.00 to 96.005, thenthe half tick value can be similarly identifiedas follows:

Calculating basis point value or tick valuesfor other STIR futures contracts The other STIR futures contracts have their tickvalues calculated in a similar fashion.

Three Month Sterling (Short Sterling)Interest Rate futures contractFor example, for the Short Sterling contract, theonly difference is that the nominal contract valueis £500,000.Therefore the tick value of a “01”can be calculated as follows:

Three Month Euro Swiss Franc(Euroswiss) Interest Rate futures contractFor the Euroswiss, the tick value is similar to theEURIBOR contract, in that the nominal contractvalue is of a similar denomination ieCHF1,000,000.Therefore:


Three Month Euroyen (TIBOR) InterestRate futures contractFor the Euroyen, the tick value is larger, becausethe nominal contract value is greater:

Therefore

STIRs as “contracts for difference”The tick values created above represent adealer’s actual profit, or loss on the transaction.

Consequently, such profit and loss amounts willshow up on a balance sheet, as they represent areal ‘cash’ flow.

Hence a dealer using STIR futures contracts istrading interest rate risk, however, without theassociated risks of On Balance Sheettransactions, such as when trading the underlyingcash inter-bank market.The only sum that wouldappear on a Bank’s balance sheet, when tradingfutures contracts, is the profit or loss therebygenerated. Hence, this is why STIR futures arealso known as: “contracts for difference”

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Now that we have looked at minimum tickmovements of STIR futures contracts, it isimportant to see what a price movement up, ordown, actually implies, in interest rate terms.

The following diagram portrays, in pictorial style,the relationship between interest rates, and theirrelated STIR futures contract.This will bereferred to within the text of this section.

BUYING a Future is like “lending”* at thatequivalent interest rate.

SELLING a Future is like “borrowing” at thatequivalent interest rate.

*Lending in the cash market would normally be at London Inter-bank Bid Rate (LIBID) or equivalent.

Buying, or selling, STIR futures? So far, we have only looked at futures contractspurely in terms of the value of ‘minimum tick sizemovements.’ This would enable you to calculateprofit and loss.

For example:

Step 1: Buy 5 EURIBOR contracts at 97.60,Step 2: Sell 5 EURIBOR contracts at 97.70

Calculate Profit/Loss on transaction as follows:5 (contracts) x 10 ticks x €25.00 per full tick=€1,250.00 (profit)

Bought low and sold high, so it is a profit.

However, you also need to consider why a traderbuys, or sells, a STIR contract and what thisimplies in interest rate terms.

Firstly, it is important to realise that STIR futurescontracts trade on a price that is directly‘inverse’ to interest rates. For example:

Typical futures price

Bid Ask (Offer)

97.205 97.210

The interest rate implied from this indirectmethod of pricing can simply be found by takingthe price away from 100. Hence:

Bid Ask (offer)

100.000–97.205 100.000–97.210

Implied

interest rate: 2.795% 2.790%

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Price movements of STIR futures contracts l ll6

Figure 2: STIR Futures Diagram

Therefore:

A price for the September sterling futurescontract, of say 97.00, implies that the market’sperception is that the official three monthLIBOR fixing on the 3rd Wednesday ofSeptember at 11 am will be 3%.

l The BuyerA trader wishing to buy the STIR futures onLIFFE CONNECT®, ie simply taking the viewthat the price will be higher (ie impliedinterest rates lower) is termed aspeculator.

The trader could therefore either:a) specify a price at which they wish to buy

(perhaps join the bid at 97.000), orb) enter a “market” order to buy (ie take

the best available offer at say, 97.005).

Buying a STIR is like lending12 at the equivalentinterest rate, (ie in this case 2.995%.)

l The SellerA trader wishing to sell the STIR future onLIFFE CONNECT®, ie simply taking the viewthat the price will be lower (ie impliedinterest rates higher) is also said to be aspeculator.

The trader could therefore either:a) specify a price at which they wish to sell

(perhaps join the offer at 97.005) orb) simply enter an order to sell (ie “hit the

bid” at 97.000).

Selling a STIR is like borrowing at theequivalent interest rate, (ie in this case 3%.)

Hence,

A trader buys STIR futures when he thinksinterest rates are going to FALL.(ie said to be “bullish” for interest rates.)

Whereas, a trader sells STIR futures whenhe thinks interest rates are going to RISE (iesaid to be “bearish” for interest rates)13.

Furthermore, rather than simply speculatingon future price movements, a dealer couldbe using STIR futures as either a hedge ie toprotect an underlying cash position. (We willlook at an example of a hedger shortly.)

l The concept of “Long” and “Short”in STIR futuresWhen a dealer first initiates a new STIRposition, either to buy or sell, he is said to:

Go “long” if he buys the contract.

Or

Go “short” if he sells the contract.

The concept of “going short” can thereforeseem strange, ie selling something that onedoes not own, especially since there is notangible underlying product here. However,the position can either be closed out, bybuying back at a later date, or simply holdinguntil expiry and paying, or receiving, a cashdifferential based on the official fixing of theLIBOR/EURIBOR/TIBOR rate, this final priceis known as the EDSP (Exchange DeliverySettlement Price) of the relevant futurescontract.


12 Beware of the concept of lending at that rate, since STIRS are all based on a LIBOR rate, whereas in the underlying cashmarket lending would have to be transacted at LIBID, or equivalent rate. For hedging purposes, this would always make asynthetic (ie futures) transaction (where you have bought the future) appear more attractive than lending in the underlying cashmarket where you would be dealing at the prevailing LIBID rate.

13 “Bullish” in most markets means up, but in interest rate markets, it means interest rates lower, similarly “bearish” in mostmarkets means down, but in interest rate markets it means interest rates higher.

Adding to a position, (ie buying more, if one islong, or selling more, if one is short), simplyadds to this “long” or “short” position.

It is not until a trader actually takes an equaland opposite position in the contract, thathe is said to be “square” or “flat” (ie has noposition).

It is important to realise too, that a traderdoes not have to hold a position until expiryof the contract, but can trade out of aposition at any time up until expiry. He cando this by buying (selling) an equal andopposite transaction in the futures marketto the position already held.

The pricing mechanism of STIR futuresSo far we have only looked at the STIR futurescontracts with a given price to work from. Buthow is the price actually derived?

As one would expect, STIR futures are pricedfrom the underlying cash inter-bank moneymarkets from which they derive.

Prior to the introduction of STIRs (and FRAs –Forward Rate Agreements that trade in the OTCmarket) a dealer in the cash markets could easilyfind himself with so-called ‘mis-matched’ positions.

For example, suppose a dealer in the inter-bankmarket had lent six month cash and then foundthat he could only borrow for the first threemonths at an acceptable rate. He therebycreated for himself an exposure, ‘borrowingrequirement’, relating to a three month period,but starting in three months time ie‘forward/forward’.

The term ‘forward/forward’, therefore literallymeans an exposure starting on a forward date,for a further period of time.

It was because of the headaches associated withrunning these ‘mis-matched’ positions thatdealers soon devised a market for dealing‘forward/forward’.

By using a simple mathematical formula, knownas the ‘forward/forward formula’, they were ableto calculate the interest rate they would need toobtain for the forward period, in order to ensurethat they did not lose money on the cashtransaction as a whole.

Furthermore, since futures are concerned withthe implied value of interest rates for a givenperiod, this so called ‘forward/forward formula’can also be applied to the pricing of STIR futuresand works in exactly the same way, as shownbelow:

The forward/forward formula

Where ‘a’ is the long date, ‘b’ is the short dateand ‘c’ is the forward/forward period.

The formula for calculating ‘c’ (the unknown)is therefore:

NB. *If the contract to be priced is theShort Sterling contract, you must rememberto replace 360* with 365 in the above formula.(All other STIR contracts are calculated usinga 360-day basis.)

Since STIR Futures are based on either aLIBOR/EURIBOR/TIBOR rate, you must nowdetermine which information would be neededto create a LIBOR/EURIBOR/TIBOR rate forthe future period ‘c’.

b

a

c?

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The following diagram shows how this wouldbe created:

Explanation:

Assume a trader has borrowed cash for sixmonths (ie ‘the long date’,) and only lent cash forsay three months (ie ‘the short date’.) By usingthe forward/forward formula, the trader is ableto calculate the rate at which he has effectivelyborrowed for the 3–6 period.

This so-called forward/forward formula canbe used to calculate the ‘value’ ofLIBOR/EURIBOR/TIBOR from any given startdate and for any given LIBOR/EURIBOR/TIBORperiod, and since STIR futures are based on thevalue of LIBOR/EURIBOR/TIBOR, it can be usedin this context.

Example: Pricing STIR futures off the cashmoney market ratesAll STIR futures are essentially priced off theCash Inter-bank Money Market rates (with slight‘sentiment’ adjustments, as you shall see).This isbecause the forward/forward formula needsCash rates in the first instance to give a roughapproximation of what the implied forwardinterest rate should be.

For example:

* = 3rd Wednesday of contract delivery month

Assume today is Tuesday 22nd March 2005(Spot date, for calculating implied EURIBOR

interest rate futures from the Cash rates,is therefore Thursday, 24th).

NB: If this were a Short Sterling example, itwould trade ‘out of today’ (T + 0), not spot.

To calculate the implied, or fair value, price forthe June ’05 EURIBOR futures contract using theforward/forward formula:

Given:

6 month cash rates: 2.2735 – 2.1485 (use offeredside ie “Borrow” long date)three-month cash rates: 2.1486 – 2.0236 (use bidside ie “Lend” short date)

Although there are various methods of creatingthis rate, including creating a trading channel, thisis probably the simplest method to create theimplied forward/forward borrowing(ie EURIBOR) rate.

This is because, if you use the “borrowing rate”for the long date (here 173 days) and thenuse the “lending rate” for the short date(here 83 days), you thereby create a syntheticimplied rate, at which one could “borrow”the forward/forward period.

Since STIRS are based on what the impliedborrowing rate should be (eitherLIBOR/EURIBOR or TIBOR depending on thecontract concerned), it can then be used in thiscontext to create a “fair” futures price.

Diagrammatically it would look like this:

For “c” use 91 days for Short Sterling (ie 1/4 of365 days), but 90 days for all other STIR futurescontracts (ie 1/4 of 360 days).Thus 90 days from


15/06/05 = 13/09/05, ie not always the next‘futures’ date (21/09/05).

Now, using forward/forward formula

= 2.49% (Implied forward/forward BorrowingRate)

Therefore, the implied or ‘fair’ futures price forthe June EURIBOR (ie three-month EURIBORfrom Monday preceding 3rd Wednesday14 of June)should be 100 – 2.49 = 97.51.

However, this is not to say that the futures pricewill always be trading at this exact rate.

For example:

The fair futures price might be 97.510, but theactual futures price might be trading in themarket at say 97.540.

This differential cannot be mathematicallycalculated, but can be attributed to “marketsentiment.” In the example above, it was onlythree full basis points or ‘ticks’.

However, if the differential was too wide, thenthere could be an arbitrage opportunity (ierisk free profit) and cash/futures traders wouldquickly arbitrage between the two markets, thusclosing any such gap.

The Basis‘The basis’, sometimes referred to as ‘simplebasis’, is the term given to:

The difference between the current three-monthLIBOR/EURIBOR/TIBOR rate, trading in the cashmoney markets and the actual futures price ofthe corresponding STIR contract.

For example:

Three month EURIBOR cash trading at: 2.1486%Actual nearest three month futures trading at:2.195% (ie price of 97.805)

Basis (or simple basis):-0.046415 (ie 4.6 basis points)

‘The basis’ can trade higher, or lower, over thelife of the futures contract, due to the nature ofsupply and demand and this is known as ‘basisrisk’. However, the only thing you can say withsome certainty is that:

At expiry of the futures contract, the cash threemonth LIBOR/EURIBOR/TIBOR rate and theExchange Delivery Settlement Price (EDSP)of the futures contract will converge (ie bethe same) and the basis will be zero.

However, a “hedger”16 must always be awareof “basis risk”, during the life of the contract(s)being used for hedging purposes.

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14 Trades “out of SPOT” – so will actually stop trading on the Monday preceding the 3rd Wednesday.15 The basis is “negative” when the interest rate implied from futures pricing is lower than the cash price.16 see notes on hedging.

“Basis risk”

“Basis risk” therefore concerns the differencebetween futures pricing and the price of theunderlying cash money market instrument fromwhich it derives (this is true of any futuresmarket, not just STIR futures contracts).

ConclusionThe previous example served to illustrate howa STIR futures price is derived from cash rates,using the forward/forward formula.

Hence:

If cash money market rates move, then byimplication, STIR futures prices will also move,and vice versa.

The price of STIR futures contracts are nottherefore, simply based on what traders “think”the price will be in the future, but are based onmathematical principles.

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Futures (and options) can be used for three mainpurposes:

1. To hedge2. To speculate3. To arbitrage

l Hedger – definition“A Hedger uses the market to offset, cover,or protect, either an actual underlyingposition, or a perceived requirement.

A true hedger therefore, does not seek toprofit from a hedge, but simply takes aposition as a form of insurance, to cover aposition in one market, or product, with anequal and opposite position in another.

A “perfect hedge” should therefore result ina profit in one position being fully offset byan equal and opposite loss in the other.”

In simple terms:

‘Protection against a fall in interest rates can beachieved by buying futures’; ie a so-called “long”hedge, and, ‘Protection against a rise in interestrates can be achieved by selling futures’, ie aso-called “short” hedge.

l Speculator – definitionA Speculator uses the STIR market to simply“buy low” and “sell high” or vice versa,thereby hoping to make a profit from thedifference in price.

A speculator therefore has no real need ofthe underlying product concerned and canspeculate on any contract.

However, it must be remembered that aspeculator performs a very useful purpose –that of providing much needed liquidity(ie lots of buyers and sellers at any givenprice) to any futures contract.

l Arbitrager – definitionProducts that have identical characteristicsand so are perfect substitutes for each other,should theoretically trade at the same price.If they do not, a risk free profit can beobtained by simultaneously selling the higherpriced one and buying the lower priced one.

An “arbitrageur” is therefore someone whouses the markets to take advantage ofpricing anomalies that may occur.

This could be between two inter-relatedproducts on the Exchange, two inter-relatedproducts on two different Exchanges, orbetween say, an Exchange traded product andthe same product trading in the OTC market.

The main point to remember aboutarbitrage, is that:

it can only be defined as “pure” arbitrage,if both sides of the transaction are dealtsimultaneously (ie there is no risk at any time).

Any delay involved (perhaps waiting for oneside to move more than the other), is knownin the markets as “legging risk” or “lifting aleg” and is not pure arbitrage – as anelement of risk has thereby been introduced.

Using STIR futures contracts as a hedgeMany traders use STIR futures contracts tosimply speculate on future price movements.However, it is important to realise that a futuresposition can also be used to hedge (ie cover, orprotect) an underlying cash position.

Here we will look at an example of a CorporateTreasurer, hedging a Sterling (£) cash loan usingSTIR futures.

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Trading with STIR futures l ll7

This particular example would be considereda “perfect hedge” ie the dates match exactly.

Scenario 1On 15 March 2005, a Corporate Treasurerborrowed £10 million in the inter-bank marketfor three months, due to be rolled-over on15 June 2005 (3rd Wednesday). It is now a monthon,April 2005, and the Corporate Treasureris worried that interest rates will rise betweennow and June.

Therefore, the Corporate Treasurer has a needto “hedge” this exposure of £10 million against arise in interest rates when he rolls the positionover in June.

The Corporate Treasurer has a borrowingrequirement that starts in two month’s time,for a further period of three months.Therefore,rather than just wait until the next rollover date(June 15th), he could use STIR futures contractsas a hedge, against an anticipated adverse(ie upward in this case) move in interest rates.

The June Short Sterling contract is concernedwith the value of three month LIBOR from the3rd Wednesday of June, which, in this case,happens to match the Corporate Treasurer’scash rollover dates perfectly.As such, theCorporate Treasurer decides to hedge his cashexposure with the June Three Month Sterling(Short Sterling) Interest Rate Futures contract.

The price on the Euronext.liffe LIFFECONNECT® screen for June ’05 is, say,‘95.020(bid) – 95.030 (offer)’.

The Corporate Treasurer therefore sells 20Three Month Sterling (Short Sterling) InterestRate Future contracts (ie £10m divided by£500,000 per contract = 20 contracts) at 95.02(as he wants to protect himself from interestrates going up). Hence he has thereby effectivelyhedged (ie protected) his borrowing cost for the

next roll-over date at this equivalent interestrate level ie 100 – 95.02 = 4.98%).

Let us now consider the outcome of both thefutures contract and the underlying cash loan.A “perfect hedge” should mean that what hemakes on the futures contract, he loses on theunderlying cash position and vice versa.

l The STIR futures contractOn the Settlement Date of the futurescontract (ie 11 am on 15 June 2005), we willassume the Corporate Treasurer wascorrect, interest rates have risen and theEDSP, (Exchange Delivery Settlement Price)is 94.51 (5.49%). Based on the ‘tick’ sizemovement used for settling STIRS, theCorporate Treasurer would make a profiton his futures position as follows:

20 (no. of contracts) x £.12.50 (minimumtick size) x 51 (number of ticks) =£12,750.00 profit

l The LIBOR-linked loanOn 15 June 2005, when the CorporateTreasurer comes to roll-over his loan,interest rates have risen and the new threemonth inter-bank offered rate quoted to himalso happens to be 5.49% (exclusive of anycorporate margin that may be added on).

If the Corporate Treasurer had not hedgedhis cash position in the futures market, hewould now be in the position of having tofund the higher cost of the loan. However,because he effectively ‘hedged’ himself in theFutures market, he can now use the profitfrom his Futures position (£12,750) to offsetthis higher borrowing cost.


Indeed, the net effect of the profit received fromhis futures position, is to reduce his overallborrowing cost (exclusive of dealing costs) to4.98% which was the implied rate at which heoriginally dealt in the Futures market.

We can prove this as follows:

Actual borrowing cost:

Versus expected borrowing cost:

Difference:-£12,854.79Less profit received on Futures contracts:£12,750.00Loss on hedge:-£104.79*

*This tiny loss on the transaction is due to the actual/365 daynature of the Sterling market, versus the “1/4 of a year”nature of the futures market.A perfect hedge does notseek to make a profit or a loss from the transaction.

Hedging where dates don’t match, ie tonon-Euronext.liffe settlement datesThere are two ways of hedging using STIRSwhere the roll-over dates don’t match.

1. Hedging to the closest futures date2. Ratio hedging using two futures

contracts dates

1. Hedging to the closest futures date Using the previous example of a CorporateTreasurer with a borrowing requirement of£10,000,000, assume it is now 10 June 2005and the date to be hedged to is 1 September2005.The Corporate Treasurer decides tohedge his position just using the SeptemberFutures contract, which actually expires onthe 3rd Wednesday of the contract month.

As the dates of the rollover of the position andthe expiry of the Futures contract which is beingused to hedge the position do not match, thehedge will not be a perfect hedge.

The first thing the Corporate Treasurer must donow is to estimate what “the basis” is likely to beon the date when the hedge is to be lifted.Theaim here is to calculate a more realistic targetrate for the implied borrowing rate, using STIRfutures contracts.

Based on the assumption, (not always correct),that “the basis” will converge to zero fromnow until the expiration of the futures contract,in a linear (ie straight line) fashion, it is possiblefor the Corporate Treasurer to estimate whatthe basis will be on the date that the hedge is to be lifted ie 1 September 2005.

Example:The Corporate Treasurer will be rolling over athree month £10 million loan on 1 September2005 (ie he has a borrowing requirement)and wishes to protect himself now againstwhat he sees as an anticipated adverse risein interest rates.

He could cover this risk now by selling STIRfutures.

Given:l current Date 28 Junel three month £ LIBOR 4.903%

(95.10 equiv. futures price)l six month £ LIBOR 4.976%l September futures price 95.04

(ie 4.96%)

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Hence the basis (ie difference betweencurrent three month LIBOR and impliedthree month LIBOR) from September =95.10 – 95.04 = + 0.0617

l Estimating the basisThe Corporate Treasurer must nowcalculate his “target” borrowing rate. Inorder to do this it is necessary to estimatewhat the basis will be on 1 September 2005– ie the date the hedge is to be lifted.

The formula is as follows:

Where:

l the basis period = the time from thedate the hedge is lifted, until the futuresexpiration date

l the hedge period = the time from thedate the hedge is put on, until the datethat the hedge is lifted.

Diagrammatically it would look like this:

Therefore:

The Treasurer must now incorporate this figureof “+0.01” into his expected borrowing ratecalculation, as follows:

Borrowing rate implied by futures price (95.04),minus* expected basis of +0.01:= 4.96% (ie 100 – 95.04) – 0.01= 4.95%

*If the basis was a negative figure, then this would be addedto the total.

l OutcomeOn 1 September let us assume that threemonth LIBOR has risen to 5.01% and theSeptember futures price has fallen to say94.98 (reflecting a basis of 0.01 ticks).As aresult, the Corporate Treasurer’s effectiveborrowing rate is now:

= three month LIBOR – futures profit= 5.01% – 0.06% (ie difference between

original futures price 95.04 and newfutures price 94.98)

= 4.951%

l ConclusionIn the above example, the CorporateTreasurer’s realised cost of funds was equalto the target rate of 4.95%, since the basison the day the hedge was lifted was exactlyequal to the estimated basis of 1 ticks.

However, it should be realised that the abovemethod for estimating basis can only serveas a rough approximation of the level of thebasis on a given futures date.This is because,in practice, basis does not always convergeto zero in a linear (ie straight line) fashion.

2. Ratio hedging using two futurescontract dates An alternative method of hedging anexposure where the maturity dates ofEuronext.liffe STIR futures contracts do notmatch the date(s) of the exposure beinghedged is using the technique of ratiohedging.

Rather than just targeting one futures date, ahedge can also be “interpolated” (ie straightline forecasting) between two futures dates.

Expected basis at the end of hedge = basis periodhedge period + basis period


17 the basis is said to be “positive” when the interest rate implied from futures price is higher than the cash price.

This can prove particularly effective where:

a) the hedge is for a date that falls right in themiddle of two futures dates (especially if theperiod concerned is some distance away),and also

b) if the sum to be hedged is of a reasonablesize.

An example will illustrate this:

ExampleA dealer wishes to hedge €100m.This time theperiod to be hedged is a three month EURIBORborrowing rate, but starting in 9 months time.

Given:l Current Date 19/07/05l Spot Date 21/07/05

The actual dates are therefore:l Start Date 21/04/06l End Date 21/07/06.

Diagrammatically the period concerned sitsbetween the following futures dates:

“Linear interpolation” shows that 61 days of thedeposit period (ie from 21/04/06 – 21/06/06)falls in the March futures (90 day18) contractperiod. Similarly, the remaining 30 days of thedeposit period (ie from 21/06/06 – 21/07/06)falls in the June futures (90 day) contract period.

Hence for hedging purposes, the ratio of futurescontracts for a particular month to use would bethe number of days in a deposit period divided

by the number of days in the futures period,multiplied by 100, this can be represented:

Where ai is the ratio of futures contractsneeded for a specific month, bi is the number ofdays of the deposit period in the specific futuresperiod and ci is the number of days in thespecific futures period.

Therefore, for the ratio of contracts to use forthe March futures contract would be:

And, the ratio of contracts to use for the Junefutures contract would be:

In order to calculate the number of futurescontracts in each month, the ratio of futurescontracts, as calculated above, ai, needs to bemultiplied by the amount to be hedged dividedby the contract size of the futures contract.

Therefore, for the March futures contract:

And for the June futures contract:

Therefore, the hedge ratio would involve selling68 contracts in the March futures contract andselling 33 contracts in the June futures contract.This is in contrast to the previous example,where all of the hedge was put into one futurescontract.


18 If contract concerned is Short Sterling then the futures period assumed would be 91 days, all others 90 days.

However, this ratio hedge would still encounterbasis risk, and would therefore need to bemanaged very closely.

As the position moves forward in time, and getscloser to expiry of the March futures contract(15th), a rollover of the 68 contracts, fromMarch into June (e.g. by buying back March andselling June) would have to be completed.

This is because the hedge needs to be in placeuntil 21st April.At the time that the Marchposition is rolled over into June, a “target rate”could then be calculated for the hedge (themethod as given in the previous example).

Trading the futures curve using‘calendar spreads’As well as establishing positions in eachindividual STIR futures contract listed, it is alsopossible for a trader to utilise ‘calendar spreads’.

This implies trading one contract month againstanother.A calendar spread is generallyconsidered less risky than taking an outrightdirectional position in any one of the contracts.

For example:If the current cash yield curve on a givencurrency (say euro) is positive, ie short terminterest rates are lower than longer terminterest rates, then this will be reflected in theEURIBOR futures curve.That is to say, near term(‘front month’) STIR futures prices will be higher(implied interest rates lower) than subsequentcontract months.

Assume it is now May 2005, and the prices forthe quarterly EURIBOR futures contracts are asfollows:

June ’05 Sep ’05 Dec ’05 Mar ’06

97.550 97.400 97.395 97.215

A trader might expect the positive yield curve,implied in the figures above, to move moresharply positive (that is, perhaps near-term STIR

prices to stay static, but longer-term STIR pricesto move lower (ie interest rates higher)).

A trader can simulate this trade in the futuresmarket, by buying the near date contract (sayJun ’05 at 97.550) and selling the far datecontract (say Mar ’06 at 97.215), at a differentialof + 33.5.This type of strategy is known as:‘buying the spread’, ie buy near date, sell fardate.

Conversely, if the trader expects the longer termrates to fall, relative to near term rates, then hecould do the opposite.That is, sell the near date(say Jun ’05 at 97.550) and buy the far date(this time say Dec ’05 at 97.395) at a differentialof + 15.5.This type of strategy is known as:‘selling the spread’ ie sell near date, buyfar date.

Strip hedge or stack hedge If a trader uses the STIR futures market to hedgepositions already held, he can do so in a numberof different ways.

l The strip hedgeA ‘Strip Hedge’ is where a trader uses anumber of different contract months tohedge a position.

For example:Using a combination of say, the Jun ’05, Sep’05 and Dec ’05 and Mar ’06 STIR futurescontracts, (ie 4 x 3 months = one year) tohedge a one year rate that commences inJune 2005.This is known as a ‘strip’ hedge,because the trader is using a ‘strip’ of futurescontracts, to replicate a one-year rate.

l The stack hedgeThe ‘Stack Hedge’ is where a trader uses justone futures contract month to hedge a

l


position that, in order to cover the periodconcerned, would normally require aconsecutive series of futures contractmonths to be bought (or sold).

For example, compared to the example givenabove, a trader might use only the June ’05contract to hedge the one-year rate (ie 4 x June contract).

This is known as a ‘stack’ hedge, because thetrader is effectively stacking up all of theposition into one contract month only.However, in this instance a trader wouldneed to remember to roll-over each of thecontracts as it expired and be aware of thebasis risk!

Other possible spread trades availableto trade at Euronext.liffe include:Trading the relative movement of STIR ratesbetween two different currencies ie sayEURIBOR versus Short Sterling.This could bedone by taking a long (short) position in theEURIBOR contract and doing the oppositeie short (long) in the Short Sterling futurescontract.

Here, although a 1% move up or down is similar,the different contract sizes and also anyexchange rate fluctuations (£ versus €) wouldalso have to be taken into account.


Interest Rate swapsInterest rate swaps (IRSs) are OTC (Over theCounter), Off Balance Sheet, derivativeinstruments.They are concerned with theswapping of interest streams, or “cashflows”,between two counterparties, on a notionalprincipal amount, over a given period of time.

Market terminology Fixed versus Floating – The ‘Coupon’ Swap

The most basic type of swap is the so-called“plain vanilla “ or “coupon” swap, where the twocounterparties to the swap are swapping from a“fixed” rate of interest, agreed at the outset, to a“floating” rate of interest, or vice versa.Thefloating reference rate is normally either three,or six month, LIBOR/EURIBOR.

l So why do the swap?With an Interest Rate Swap, the ‘product’being ‘swapped’ is one form of interestpayments (usually a fixed rate), for another(usually a floating rate.)

The two parties to the swap are therefore takingopposing views about the future direction ofinterest rates.

One party to the swap:“the payer of fixed/receiver of floating” thinksthat interest rates will increase over the periodof the swap (and therefore hopes to makemoney from this stance).

Whilst the other counterparty:“the receiver of fixed/payer of floating” thinksthat interest rates will fall over the period of theswap, (and likewise hopes to make money fromthis stance).

The two counterparties to the IRS transactionare therefore simply ‘swapping’ differences ininterest streams (ie cashflows), on a nominalamount, over the life of the swap. Hence IRS’sare considered “Off Balance Sheet” because thenominal underlying capital sum is not at risk.

However, it is important to realise that:At the time the swap is agreed, the twoprojected cashflows are worth the same.Thus, they are said to ‘value to par’

Looking at a typical IRS price:‘4.14/4.17’

To a market maker (ie the bank making theprice) this means that:

At ‘4.14’ elects to:pay a fixed rate of interest (on euros‘nominally’ borrowed) and also receive afloating rate of interest (on euros ‘nominally’lent) ie “pays fixed” at the lowest ratepossible

And:

At ‘4.17’ elects to:receive a fixed rate of interest (on euros‘nominally’ lent) and also pay a floating rate ofinterest (on euros ‘nominally’ borrowed) ie“receives fixed” at the highest rate possible

l So why do the swap?Although IRS’s can be used for eitherhedging, or speculative purposes, essentially:

The two counterparties to an Interest RateSwap, enter into the transaction becausethey have opposing views on the futuredirection of interest rates.

The reason why the value of one side of theswap can increase or decrease, versus theother side, is because it compares fixed,versus floating, interest rates.Thus bydefinition, the fixed side cannot change overtime (ie it is ‘fixed’ at the outset), but thefloating side certainly can.This is because the

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Pricing swaps using STIR futures -Interest Rate swaps l ll8

floating side is assumed at the outset, butcan only actually be agreed on the specificLIBOR/EURIBOR rollover dates.

The relationship between STIR futuresand short dated IRSsEuronext.liffe lists a suite of both € and $denominated swap futures contracts,€ Swapnote® and $ Swapnote® as well as theThree Month Euro (EURIBOR) FuturesContract.Within this publication we shall confineour explanation of IRSs to the euro denominatedswaps market.

Short Dated Interest Rate Swaps are closelyrelated to the STIR futures market and this canbe seen more clearly when two aspects of swapstrading are introduced;

a) the “cashflows” that change hands on aswap; and

b) the way in which “par value” on a shortdated swap can be determined

In order to demonstrate this, you will look athow the price of a one-year interest rate swap isdetermined; and also see how much moneyactually changes hands, on the given ‘rollover’dates.

The diagram below illustrates one of the mostbasic types of coupon swap, the so-called

“One Year Annual 3s”.

This is a swap where one annual rate of interest(on a nominal underlying principal amount) isswapped for four three monthly floating rates(the “3s”).

The fair price of the swap rate is determined bythe return that the four x three monthly ratesare likely to produce over the one year period(ie the swap will be said to “value to par”). Forexample, the price of a one year eurodenominated swap is determined by knowing thecurrent spot three month euro cash rate (ie theinter-bank market can tell you this) and the

implied three month rate for the second, thirdand fourth successive, three month euro periods.

Since STIR futures are concerned with impliedEURIBOR rates from a future given date, theycan be used in this context. Hence it can be seenthat short dated swaps are priced off the so-called “futures strip” ie the sequential list ofthree month STIR futures prices following thefirst three month cash period.

In fact short-dated IRSs are priced off STIRfutures prices for as far out as good liquidity willallow. It is only when one gets to so called“longer dated swaps”, ie 3 – 20 years +, that IRSare no longer priced off the STIRS futures strip,but are then priced off the relevant “benchmark”Treasury bond markets.

Using STIR futures strip to determine theprice of a one year swap rate:

To calculate the one-year Swap rate fromthree-month cash and three STIRS.

One Year Fixed (Annually) vs.Three Monthfloating (EURIBOR)

*assumed EURIBOR rate

To prove:That the fixed rate applicable above (as yetunknown) is determined by the floating rate cashpayments forecast.

Hence we must find the sum total of the four xthree month EURIBOR (ie floating rate)payments, (on the rates given above), at the timeof swapping, and apply this rate as the oneannualised rate.

l

l


At this point we should find that the cashflowswill “value to ‘par’ ” ie both be worth the same.

GIVEN:Today is 13 June 2005, and assume rates givenare as follows:

Three month CASH (EURIBOR) = 2.50% Sep ’05 EURIBOR futures = 97.45 (2.55%)Dec ’05 EURIBOR futures = 97.33 (2.67%)Mar ’06 EURIBOR futures = 97.28 (2.72%)

Swap formula:

Where: i = swap rate

a, b, c, d = rate of STIR Future (or FRA*if using linear interpolation) for eachperiod

n = number of compounding periods inswap rate.

Therefore:

Note. In order to isolate the value of the swaprate “i” (mentioned above) on the left hand sideof the equation, all other parts must be removedto the right hand side of the equation, followingthe “change the side/change the sign” rule ofmathematics.

Hence “1 +” on the left hand side of the formula,now becomes “ -1” on the right hand side (seebelow), similarly “divided by 100” becomes“multiply by 100!”and “364/ 360” becomes“360/364”. Each bracket on the right hand sideis nothing more than simple interest on anominal “1”.

For example, in the first bracket,“1.006388889”really means interest on €1m would be€6,388.89. Hence, the equation now looks likethis:

= 2.636% (Annual Actual/360) moneymarket basis*

*If the rollover dates are not in line with thefutures strip, then three month cash andsubsequent FRA (Forward Rate Agreement)prices (ie 3 – 6, 6 – 9 and 9 -12’s) can besubstituted. (The brackets being side by sidejust means that you must simply multiply themtogether ie 1.006388889 x 1.006445833 etc.)

Having found an equivalent annual rate, ie 3.66%,it is now possible to check whether thisis correct. If it is, then the cashflows on the swap,ie fixed versus floating, should ‘value to par’(ie both be worth the same).


To prove:Alternative A:

OR

Alternative B:

Therefore, at the end of the 4 x 3 monthlyperiods,Alternative B, provides total projected(ie assumed) cashflows on the nominal €1m swap of:

= € 26,724.46

Therefore:A. 1 x Annual Rate = € 26,726.11B. 4 x Quarterly Rate = € 26,724.46

1.65 difference19

Therefore, the swap “values to par” as the twoprojected cashflows are worth the same.

Hence the fair fixed rate on the swap cannow be inserted as follows:

*Assumed EURIBOR rate.

It is important to realise that the calculations for‘B’, take into account the fact that the formulaassumes interest for periods 2,3 and 4 are basedon nominal principal, plus interest, from all theprevious periods.

In reality the cashflows received from the swapcounterparty for each of the above periods(ie after 3 months, 6 months, 9 months and12 months), are just the interest on the nominalprincipal amount.The recipient must thereforeensure that they themselves re-invest eachsubsequent cashflow at the next reinvestmentrate in order for the mathematics to work.


19 This small difference is due to rounding error on the 4 quarterly rates.

ConclusionThe price of a short dated swap is determinedby the assumed (ie likely, but not definite) returnon the floating legs over the period of the swap.Hence, a “one-year annual 3’s” is determined bythe value of three months cash, and subsequentthree month EURIBOR rates.

Similarly, a two-year euro swap (two annualpayments) can be determined by three monthcash and subsequent three month EURIBORrates – although it is standard practise to quoteswaps from two years outwards against sixmonth EURIBOR (less cashflows to worryabout).

Longer dated swaps, say three years plus, tendnot to be priced off the STIR futures strip, butuse benchmark treasury bonds, particularlywhere STIR futures do not go out far enough, insufficient liquidity, to cover the swap periodconcerned.

At the time of swapping, the likely return fromthe fixed, or floating side, should “value to par” ieboth be worth the same.The “cashflows” actuallyswapped are the interest flows on a nominalprincipal amount, on roll-over dates actuallyspecified at the time the swap was enacted.

Using STIR futures as a hedge against aSwaps position As can be seen from the above, a swaps traderwill need to keep a very close eye on the STIRfutures market, since subsequent roll-over dateson the swap will be influenced by the value ofthis futures “strip”.

Furthermore, a swaps trader will almostcertainly use the STIR futures contracts (eitherone particular contract month or a strip ofprices) in order to hedge either one particularcashflow, or a series of cashflows, on a swapposition.

For example:Let us assume that it is now September.A swapstrader has elected to be a “payer offixed/receiver of floating”. He may feel that say,the third and fourth cashflows to be received onthe swap are a particular worry (ie interest ratesmay fall). He could therefore enter the STIRfutures market and buy the relevant amount ofthe two futures contracts most closely related tothe particular six month period, ie say March andJune.

In this way, he can keep the underlying swapsposition intact, but is “managing” the particularcashflows he feels most worried about via theSTIR futures market. Further more, he can also,at any point prior to the expiry of these futurescontracts, simply sell them back again, leaving theunderlying swaps position in place.


l

What is an option?If someone gave you the option to do something,what does this mean? In every day terms itmeans that you are given a choice.The choiceis usually whether you wish to do something,or not.

In financial markets, an Option means exactly thesame thing:

The buyer of a STIR option has the right, but notthe obligation, to buy or sell the underlying STIRfutures contract at a given price, within a giventime period, but at a price agreed now.

Euronext.liffe currently offers options on thefollowing STIR futures contracts:

l Three Month Euro (EURIBOR) Interest RateFutures

l Three Month Sterling (Short Sterling)Interest Rate Futures

l Three Month Euro Swiss Franc (Euroswiss)Interest Rate Futures

Options on STIR futures therefore introduce alevel of flexibility that is not available in theunderlying contracts themselves.That is, the rightto simply walk away from the transaction and letthe option expire worthless, if the underlyinginterest rate derivative market does not behaveas anticipated.

A STIR option can therefore be viewed as asecond derivative, in that it is essentially aderivative on a derivative.

Understanding calls and putsAll STIR option contracts are split into twotypes: calls and puts.

Calls:A call option gives the buyer of the call the right,but not the obligation, to buy (or “go long of”)the underlying STIR future at an agreed price, on,or before, a specific expiry date.

The cost of buying this option is known as theoption premium.

If the price of the underlying STIR futuresubsequently rises above the strike price(ie interest rates fall), then the buyer of the callcan exercise their right to buy the contract atthe agreed “strike” price. Conversely if the priceof the underlying STIR future falls, then the buyerof the call can simply abandon the option and letit expire worthless.

A put is a mirror image of a call, in that:

Puts:A put option gives the buyer of the put the right,but not the obligation, to sell (or “go short of”)the underlying STIR future at an agreed price, on,or before, a specific expiry date.

The cost of buying this option is also known asthe option premium.

If the price of the underlying STIR futuresubsequently falls below the strike price (ieinterest rates rise), then the buyer of the put canexercise that right to sell the contract at theagreed “strike” price. Conversely if the price ofthe STIR future rises, then the buyer of the putcan simply abandon the option and let it expireworthless. Hence, in summary it can be said that:

l the buyer of the call (the right to buy) –wants the price to rise, and

l the buyer of the put (the right to sell) –wants the price to fall.

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STIR options – an introduction l ll9

The advantages of buying andselling options

l Buying optionsThe most important advantage to the buyerof an option is this:

the buyer of an option, whether a call or a put,can benefit from any favourable price movement(either up (call) or down (put)) but can neverlose more than the cost of the option ie thepremium.This is because, if the underlyingposition goes against them, they can simplyabandon the option and let it expire worthless.

l Selling optionsThe seller (also known as “the writer”) of anoption (whether a call or a put), is on the otherside of the fence in that, if the option purchaserdecides to exercise their right then:

the seller of the option (whether a call or a put)assumes unlimited liability to provide (sell or

buy) that position, in return for the optionpremium.

For example:If the buyer of a call exercises, then the seller(call writer) must sell at the strike price and theseller’s loss is therefore unlimited. Conversely, ifthe buyer of a put exercises, then the seller (putwriter) must buy at the strike price.Again theseller’s loss is unlimited.

The basic elements of optionsOptions can be thought as having four basicelements, reflecting the type of buyer and sellerand their preferred outcome.This is summarisedin the table below:

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Type of buyer Wants this to happen:

Buyer of a STIR Call Price of the underlying to rise

Buyer of a STIR Put Price of the underlying to fall

Both the buyer of the call and the buyer of the put pay a premium and have rights, but no obligations, to exercise

Type of seller: Wants this to happen:

Seller (writer) of STIR Call Price of the underlying to fall

Seller (writer) of STIR Put Price of the underlying to rise

Both the seller of the Call and the seller of the Put, collect the option premium and have obligations, but no

rights, to fulfil.

l “Naked” and “covered” call, orput writingWhen a seller (writer) of a call, or put,(mentioned above) does so, as a stand-alonetrade ie without an underlying position toprotect it, this is known as “naked” call, orput, writing.This is because the seller of theoption is totally exposed to subsequent STIRprice movements.

However, if a trader sells (writes) a call, orput, against an underlying position alreadyheld, then this is known as “covered” call, orput, writing.This is simply because any gains,or losses, on the option exposure should beeither fully, or partially, offset by similar gains,or losses, on the underlying position and theconcept of unlimited liability is therebyreduced. Hence the trader is said to be“covered”.

De-coding the market jargon Euronext.liffe’s STIR options are traded asstandardised contracts on the LIFFE market’sregulated exchange. Understanding optionsnecessarily involves becoming familiar with theoption terminology used.Apart from thedefinitions of a call or a put, already given above,you must now look more closely at the variouscomponents of an option.

l What is meant by the “underlying”? The “underlying” is the actual position, thatthe option buyer (whether a call, or put) willend up with, should they decide to exercisethe option.

In the case of Euronext.liffe’s STIR options, the“underlying product” is one of Euronext.liffe’sSTIR futures contracts that have an associatedoptions contract, ie:

l Three Month Euro (EURIBOR) FuturesContract

l Three Month Eurodollar Futures Contractl Three Month Sterling (Short Sterling)

Futures Contract

l Three Month Euro Swiss Franc (Euroswiss)Futures Contract.

And a particular quarterly contract month ieMarch, June, September or December.

l What is the strike price/exercise price?The strike price (also known as the“exercise” price), is the actual price at whichthe underlying deal will be struck, should theoption purchaser (whether a call or a put)decide to exercise (take up) that right.

Options on Euronext.liffe’s STIR futures contractsoffer standardised strike prices, at regularintervals, on each of the products/contractmonths listed. In the case of the EURIBORcontract, the option strike intervals available areevery 0.125% for the first 4 quarterly months andall serial months, and 0.25% for all other months.

For example:Assume it is now May, and the price of theunderlying front (ie nearest) June EURIBORfutures contract is say 97.79.The option seriesthat relate to the June futures contract wouldinclude strikes of at least 97.50, 97.625, 97.75,97.875 and 98.00 etc.

This means that the strike prices available at anyone time are designed to “capture” the currentunderlying price level. New option strikes areintroduced if the price of the underlying moveshigher, or lower, than this range. For example, ifthe price of the underlying June EURIBORfutures contract fell from 97.79 to say 97.02,then a new menu of lower option strike priceswould be introduced based around this new(current) price.

l


Euronext.liffe ensures that new option series areopened as the price of the underlying moves up,or down.There are at least nine strike pricesalways available for Euronext.liffe’s EURIBORoption contract.

l What is the premium? “The premium” refers to the actual cost ofthe option, paid by the buyer, for the rightsgranted by that option20

It is worth remembering that these options are“tradable”.This means that they do not have tobe held until expiry, but can be bought and soldback into the market at their current value (iepremium), at any time up until expiry.

At expiry, if not already exercised, the option willbe cash settled and thereafter will cease to exist.Therefore, upon expiry, the option will be eitherworth something or nothing.

l What is meant by the expiry date?The date on which an option ceases to exist,is called the expiration, or expiry, date.

Every option has a pre-determined “shelf life”.When a trader buys an option, he musttherefore specify the expiry date he requires,after which time the option will cease to exist.

Euronext.liffe’s STIR options offer standardisedexpiry months, known as the option series.There are normally at least three option series,or months, available, relating to any one

particular underlying futures contract month(please see the individual contract specificationsfor further details).

It is important not to confuse the option expirymonths available with the futures contractmonth specified that serves as the underlying.

For example:If it is now June ’05 and the underlying futurescontract and month specified is the SeptemberEURIBOR, then there will be three option seriesmonths available ie July,August and September, allrelating to that particular futures contract month.

This means that one can buy an option on theunderlying product (ie Sep EURIBOR future) thatwill expire on a certain date in July,August, orSeptember.

A “July serial option” does not mean an optionon an underlying July (serial) futures contract.Rather, the serial option contract monthsavailable, all relate to a particular quarterlyfutures contract month.

In practice the option series relate to the next“quarter date” futures contract available asdetailed in the table below.


20 In many OTC markets, the option premium is paid up in full up-front, directly to the seller. However, with Euronext.liffe STIRoptions, the premium is not paid in full up-front, but is margined over a period of time.

STIR serial option expiry calendar

Serial Option: Underlying future:

January, February and March serial option all relate to the March futures contract

April, May and June serial option all relate to the June futures contract

July,August and September serial option all relate to the September futures contract

October, November and December serial option all relate to the December futures contract

As you can see from the above table, a Novemberserial option is not an option on a November(serial month) futures contract, but an option ona December (quarterly month) futures contract.Whereas, a March serial option is an option ona March (quarterly month) futures contract.

l ExerciseAn option is said to be exercised, when thebuyer of the option (either a call, or a put)actually takes up their right to go long (call),or short (put), of the underlying, at the agreedstrike price.

l American versus European styleoptions

In most financial markets there are two styles ofoptions that can be purchased, these are termed:

l American style; andl European style.

The definitions of these different types ofoptions are:

American style option – is an option that canbe exercised by the buyer of the option, forvalue, on any business day up to and includingexpiration.

European style option – is an option that canbe exercised by the buyer of the option, forvalue, on the expiration (end) day only.

An easy way to remember which is which typeof option is:

American = any day, European = expirationor end date only

All of Euronext.liffe’s STIR option contracts areAmerican Style options, where the option buyercan exercise their options, for value, on anybusiness day up to and including expiry.


Options can be used either as a stand-alone toolfor speculative purposes, or as an efficient riskmanagement tool for hedging purposes. In orderto highlight the benefits of using options asopposed to futures, a similar scenario to the onegiven in the futures section has been used.

Trading examples

Trading example: where interest ratesare falling It is now June ’05. A Corporate Treasurer has£10m of funds due in, in three months time, atwhich time he intends to place these funds ondeposit. He is concerned that between now andthen, interest rates may fall.

However, unlike the example given in the futuressection, the Corporate Treasurer would this timelike to have the flexibility of simply walking awayfrom the transaction, if he is wrong.Therefore, inthis instance he decides to use options, which hefeels would be more suitable than futurescontracts.This is because he wants to acquirethe right, but not the obligation, to be locked-inat a known rate.

Current rates are as follows:Three months cash 5%September 05 Short Sterling (futures contract) 94.59

He therefore decides to buy the September94.50 call (the right to go long of futures ieinterest rates lower).The premium quoted is say0.35%.The premium is quoted according to thestandard tick size value of the underlyingcontract concerned.

The option premium equates to a totalcost of:

20 (option contracts ie £10m/£500,000) x35 (ticks) x £12.50 (tick size value) =£8,750.00

The Corporate Treasurer now knows thatwhatever happens to interest rates over the

period, he cannot lose more than this premiumcost of £8,750.

If, by September interest rates have fallen, andthe futures contract is now trading at, say 95.00,then the Corporate Treasurer could exercise hisright to go long the September futures contract,at the agreed strike price of 94.50.This wouldmean that he now has a long futures position at94.50, which he could then immediately sell in thefutures market at 95.00 and make 0.50% profit.

The profit on the futures position wouldthen be calculated as follows:

20 (option contracts ie £10m/£500,000) x50 (ticks) x £12.50 (tick size value) =£12,500.00

Total profit:However, the cost of the option must also betaken into account. Deducting this from theprofit made on the futures transaction meansthe Corporate Treasurer has made an actualprofit of:

Profit from option position = £12,500.00Cost of option position = –£8,750.00Total profit: £3,750.00

This profit can then be used to offset the cost oftaking out the new underlying position in thecash market (ie lend cash).

As the Corporate Treasurer was correct in hisanticipation that interest rates would fall, hewould have been better off by simply buying thefutures contract outright for nil premium.However, if he had just brought futurescontracts, he would not have had the flexibilityof simply walking away from the transaction ifhe had been wrong.

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Trading with STIR options l ll10

Trading example: where interest rateshave risen Let us now look at the situation in reverse, tosee what the outcome would have been ifinterest rates had risen.

Interest rates have risen and the futurescontract settles at say 94.00. Now theCorporate Treasurer would simply abandon the94.50 call option (it has no value) and just losethe premium of £8,750.

However, he would now be free to go into thecash market and lend his money at a betterrate.21 The premium cost of £8,750 on the optionposition, is now partially offset by the fact thatthe Corporate Treasurer can now lend in theinter-bank market at say 5 7/8%, rather than5.41%.You will recall that 5.41% was the impliedrate of the futures contract (94.59) at the timeof taking out the option.

Conclusion Options can therefore be viewed as a moreflexible risk management tool, than the underlyingfutures contracts themselves.This is because:

The buyer of the option, whether a call,or a put:

Has limited adverse market risk (ie can not losemore than the premium cost). But, retainsvirtually unlimited profit potential from anyfavourable price movements.

Conversely,

The seller of the option, whether a callor a put:

Has virtually unlimited market risk.And, alsohas restricted profit potential (limited to thepremium received).

Exercising an optionTo determine the most profitable time toexercise22 an option, (or whether it is worthanything at all), it is important to understand therelationship between: the strike price of theoption and the market price of the underlyingSTIR futures contract.

The following terminology is used to identify thisprice relationship:

l In the money (ITM)A call option is said to be “In themoney” (ITM), if the strike price of theoption is lower than the market priceof the underlying futures contract.

For example:On a Short Sterling call option, at a strike priceof 94.50, with the underlying market trading atsay 95.00, the call option is ITM by 50 basispoints.

Conversely,A put option is said to be “In the money (ITM),if the strike price of the option is higher than themarket price of the underlying futures contract

For example: On a Short Sterling put optionat a strike of 93.50, with the underlying markettrading at say 93.00, the put option is ITM by50 basis points.

l Out of the money (OTM)A call option is said to be “Out of themoney” (OTM), if the strike price ofthe option is higher than the marketprice of the underlying futurescontract.

l


21 Lending would probably have to be done at LIBID ie bid side of inter-bank rates.There is usually a spread of about 1/8th betweenbid and offer rates in the inter-bank market, so LIBOR – 1/8th for non-bank risk = 5 7/8th.

22 Remember an American style option can be exercised at any time up until expiry.

For example:On a EURIBOR call option at a strike price of98.00, with the underlying market trading at say,97.75, the call option is OTM by 25 basis points.

Conversely:A put option is said to be “Out of the money”(OTM), if the strike price of the option is lowerthan the market price of the underlying futurescontract.

For example:On a EURIBOR put option at a strike of 97.50,with the underlying market trading at say 97.75,the put option is OTM by 25 basis points.

l At the money (ATM)In most O.T.C option markets, a call option issaid to be “At the money” (ATM), if the strikeprice is exactly equal to the market price of theunderlying product.

However, this is not true of STIR futures,because here:

An ATM option is considered to be theoption whose strike price is closest tothe price of the underlying instrument(futures contract)

For example:On a Euroswiss call option, with strikes of 98.00,98.25, and 98.50, with the underlying trading atsay, 98.35, the 98.00 call would be ITM, the98.50 would be OTM and the 98.25 would beconsidered to be ATM (ie closest to theunderlying), even though it is actually 10 ticks“In the Money”.

Conversely, on a Euroswiss put option, withstrikes of 98.00, 98.25, 98.50, with the underlyingtrading at say, 98.20, the 98.00 would be OTM,the 98.50 ITM and the 98.25 ATM (ie closest tothe underlying), even though it is actually fiveticks “In the Money”.

Limitations of using options – thecalculation of the break-even rateWhen studying options, it is tempting just toconsider the benefits of using them – the factthat the buyer of an option can simply abandonthe option and let it expire worthless. However,there is a catch.The buyer of the option mustalways bear in mind that, if he intends to run theposition to expiry, then:

The underlying price must move in the rightdirection by at least enough to recoup the costof the option premium.This is known as the“break-even” rate.

The break-even rate depends on whether a call,or a put, has been purchased.

For example:The “break-even rate” on a EURIBOR 97.75 calloption, at a premium of 55 ticks, is 98.30 (iestrike price plus option premium).

Whereas, on a EURIBOR 98.00 put option, at apremium of 35 ticks, the break-even rate is 97.65(ie strike price minus option premium).

Hence it can be said that:

The break even rate on a call is the strikeprice plus the premium paid.Whereas, thebreak even rate on a put is the strike priceminus the premium paid.

Option valuationA major difference between options and otherfinancial instruments is the way in which they arepriced. Supply and demand for the product andthe current level of underlying interest rates areonly part of the picture.

l

l


The mathematics used in the pricing of optionsis (by most people’s standards) relativelycomplex. Unlike, for example, the formula usedfor calculating simple interest on a deposit,option valuations cannot be based on certainty,but are based on “probability” theories.

It was the pioneering work of Fischer Black andMyron Scholes that, in 1973, first provided aviable mathematical method by which optionprices could be “fairly” evaluated.Their research-derived model is now known in the markets asthe Black & Scholes option-pricing model.Most (if not all) option traders will have this, orsimilar modified option pricing software in place,enabling them to assess the “fair” value of anygiven option both speedily and accurately.

However, even if you are not a mathematician –read on, in order to gain a basic understanding ofthe pricing process involved in option valuation.Firstly, it is necessary to break down thepremium into its main component parts.

Basically, an option premium consists of twoelements:l Intrinsic Value; andl Time Value.

l Intrinsic valueIntrinsic value refers to the real value (ie profit)that an option might already have built into itsprice.

In the case of a call option, the intrinsic valueis the amount by which the current marketprice of the underlying STIR future exceedsthe strike price of the option.

This is because the right to buy (call) belowthe current market level is valuable.

e.g. September 97.50 (current market EURIBOR say price of future)

August call 97.25 (strike price of (on Sept. future) ITM option)

Intrinsic value 0.25 (ie 25 ticks)of option

However:In the case of a put option, the intrinsic valueis the amount by which the strike price ofthe option exceeds the current market priceof the underlying STIR future.

This is because the right to sell (put) abovethe current market level is valuable.

e.g. December 98.23 (current marketEuroswiss price of future)

October put 99.00 (strike price of(on Dec future) ITM option)

Intrinsic value 0.77 (ie 77 ticks)of option

All option premiums follow this same basicpattern.

Referring back to the concept of “In theMoney”,“At the Money”, or “Out of theMoney”, it can be said that an “In theMoney” option, has, by its very definition,some intrinsic value, whereas an “Out of theMoney” option does not.

However, intrinsic value is neverreferred to as a negative number.

For example:March 97.45 (current marketEURIBOR price of future)

Jan call 97.75 (strike price of(on March future) OTM option)

Intrinsic value 0.00 (ie not – 30)of option

As you can see from the above example, theright to go long of March EURIBOR at 97.75,when the market is trading at 97.45, is not avery valuable right, ie there is no intrinsicvalue in the January call. However, it wouldnot be referred to as “minus 30”, but simply


zero. Intrinsic value is either a positivenumber, or zero.

“At the Money” options however, are moretricky.You will recall that an “At the Money”STIR option, is defined as one where thestrike price is closest to the underlying.Hence in practice some ATM options willhave some intrinsic value, and some won’t.

For example:June Short 95.05 (current market Sterling price of future)

June call 95.00 (strike price of(on June future) ATM option)

Intrinsic value 0.05 of option

In the example given above, the strike price,although closest to the underlying, is alsoactually 5 ticks lower than the underlying,therefore since it is a call option, therewould be profit in exercising it. Hence, it isan ATM option with intrinsic value of 5 ticks.

June Short 95.17 (current market Sterling price of future)

June call 95.25 (strike price (on June future) of ATM option)

Intrinsic value 0.00 (ie not – 8)of option

In the example given above, the strike price,although closest to the underlying, is alsoactually eight ticks higher than theunderlying, therefore since it is also a calloption, there would be no profit inexercising it. Hence, it is an ATM option withan intrinsic value of zero.

Intrinsic value is therefore relatively easy toaccess – it is simply the amount of realbenefit, or value, already built into the optionpremium.This means that intrinsic value ispresent whenever the option (whether a callor a put) could be exercised and theresulting futures position would be in profit.

However, intrinsic value can never be lessthan zero.

l Time valueTime value (also known as “Theta”) takesinto account how long an option has leftuntil expiry.

Time value can therefore be defined as thatportion of the option premium thatrepresents any value beyond its intrinsicvalue (see above).

Every option has a predetermined “shelf-life”.

For example, if you bought an August call onthe underlying September futures contract,it will expire on a certain day in August.Thusyou will have until this time to either:

a) Trade your option (ie sell it on tosomeone else in the market) since allSTIR options are tradeable.

b) Exercise it (on any day you choose, asit is an American style option

It is quite logical to assume, therefore, thatif you bought a September call option onthe September futures contract mentionedabove, as opposed to an August call option,then you would expect the premium to costmore because the time value is greater.

Below is a typical example of the prices ofEURIBOR Options.


Assume it is now the end of June 2005, and theunderlying September futures contract price is97.47.The price menu is as follows:

In the left-hand column, are the details of thevarious strike prices listed (here 12.5 ticks apartie 97.25, 97.375 etc). Now looking at the firstcolumn with a strike of 97.25, reading from leftto right, it gives details of the option premiumfor a July call (0.225),August call (0.235) and Sepcall (0.255) respectively. These call options allrelate to the underlying Septemberfutures contract.

However the next column along says Dec call(0.185). Here it should be realised that this is aDecember call on the underlying Decemberfutures contract, not the September futurescontract.Therefore, in a sense it does not belongwith the other three, as it is not an option onthe same underlying futures contract.

Similarly, looking at the puts, the July,Aug and Sepputs on the 97.25 strike September futurescontract are listed and then finally the Dec put.Again, the Dec put is a put on the underlyingDec futures contract, not the Septemberfutures contract.

l The concept of time decayThe concept of time decay is relatively easyto grasp ie the fact that a one-month optionshould be cheaper than a two-month option.For example looking at the rate sheet givenand reading from left to right it can be seenthat a July option is cheaper than an Augustoption and a September option is the mostexpensive in that series. Note that this

is true for any strike price andregardless of whether the option is a call, or a put.

However, the manner in which time decayactually works is trickier to understand.

Firstly, although an option with one monthleft until expiry will be cheaper than say, atwo-month option, it is not going to be halfthe price.

This is because, time decay doesnot decrease in a linear (ie straightline) fashion.

This concept needs expanding further.

Most traders, when looking at an option,would assume that if a one month optioncosts say £1,000, then a two month optionshould cost £2,000 and a three monthoption £3,000 etc.

However, this is not correct, since the priceof an option is influenced by a function ofthe square root of time.

A visual picture might explain this moreeasily.The diagram below shows graphicallythe effect that time value will have onpremium decay.


Strike Price Calls Puts

Jul Aug Sep Dec Jul Aug Sep Dec

97250 0.225 0.235 0.255 0.185 0.000 0.010 0.030 0.200

97375 0.115 0.130 0.150 0.135 0.015 0.030 0.050 0.275

97500 0.030 0.055 0.070 0.095 0.055 0.080 0.095 0.360

97625 0.005 0.020 0.025 0.065 0.155 0.170 0.175 0.455

Figure 3: Graph of time value decay

For example a 90-day option that moves forwardone day in time still has 89 days left ie a largeproportion of the time value remains. However, atwo-day option that also moves forward one dayin time has actually eaten into 50% of its availabletime value (ie a far bigger percentage).

Hence it can be said that:

Time decay starts out slowly, but increasesrapidly as expiration approaches.

This behaviour of an option premium, over time,also has to be factored into its price.

l Intrinsic value/time value combinedHaving considered both Time Value andIntrinsic value separately, it is now possibleto look at an option premium and break itdown into its two component parts.

Example 1:A EURIBOR Aug. 97.25 call (with the currentunderlying September futures price of say97.47) and a premium of say 0.235%.

The premium consists of:22 Intrinsic value (the right to buy at

96.25 is 22 ticks ITM)11⁄2 Time Value (the residual cost of the

option is all time value)231⁄2 TOTAL OPTION PREMIUM

And the total cost:€25 (tick value) x 23 1/2 (option premium)= €587.50 total cost

Example 2:A Short Sterling Oct 95.125 put (with thecurrent underlying Dec futures price of say95.28) and a premium of 11 ticks.

This premium can be broken down as:

0 Intrinsic value (the right to sell at95.125 is OTM)

11 Time Value11 TOTAL OPTION PREMIUM

And the total cost:£12.50 (tick value) x 11 (option premium) =£137.50 total cost

The option premium in this instance consistspurely of time value – there is no intrinsicvalue, as it is an Out of the Money (OTM)option.

l How can you measure the cost oftime value?Although all options have time value, thepremium applied to this portion of theoption premium is more difficult to assess.This is because firstly, as you have alreadyseen, time value does not decrease in alinear fashion (see previous diagram).

However, secondly:

time value is very much dependant onhow volatile the underlying producthas been in the past, as a likelyindicator of future price performance.

This volatility of the underlying will have amajor bearing on the total premium cost.

Let us consider this point from the positionof the option seller (writer):

0


He wants to price the option at such a levelthat the purchaser will be tempted to buythe option (whether a call, or a put), but thatthe option will not be exercised.

Consider the following diagrams:

Underlying Interest rate market ‘A’

Underlying Interest rate market ‘B’

From the seller’s point of view, he has thegreatest risk of being exercised against in thevery volatile market “A” than the less volatilemarket “B”.This is because the opportunity forthe price to reach certain levels (either up ordown) in market “A” is much greater than inmarket “B”.

The concept of volatility,“Vega” in optionterminology, is considered to be one of thegreatest headaches associated with timevalue

We must now look at its bearing on an option’sprice, in greater detail.

l Factors that affect the value ofan optionThe Black-Scholes model and similaroption pricing models all require certaininformation to be fed into them, on severalbasic variables, in order to calculate the ‘fair’price of an option. Some of these elementsare known, whilst one is unknown, asfollows:

– The current price of the underlying ‘Known’

– The strike price of the option ‘Known’– The time to expiry of the

option (theta) ‘Known’– The implied volatility of the

underlying instrument ‘Unknown’

Since the value of an option premium is afunction of all of the above variables, anychange in one of them will affect the optionpremium.

Of the above variables, the only one thatis unknown and therefore has to be“guesstimated” ie implied, is volatility(or vega).

Since the volatility of the underlying playssuch an integral part in determining theprice of an option, it can be said that:

The implied volatility of an option will be,in the end, the main factor in determiningthe actual cost of the option.

l Understanding volatilityVolatility (vega), in its most basic sense, refersto the rate of fluctuation of market prices.

It measures the variability, not theoverall direction, of the price of theunderlying instrument.

Hence markets that move slowly (in eitherdirection) are said to be “low volatility”markets, whilst markets that move quickly(in either direction) are “high volatility”markets.Volatility (sometimes simplyreferred to as “vol”), therefore measuresprice changes, but takes no account ofdirectional price movements.


For example:A 10% volatility figure means that the price ofthe underlying is expected to move, up, ordown, by 10% from its current market level,over the period concerned. Increasing thevolatility of the underlying instrument willtherefore have the effect of increasing theoption premium demanded, whether for a callor a put (ie more risk of being exercised), allother things being equal.

Understanding delta and gamma As well as understanding the basic principlesof trading options, it is important to beaware of some of the other jargonassociated with option trading.

l DeltaThe delta of an option measures:

“the rate of change of an option, given a oneunit change in the price of the underlying”

But what does it mean? The delta of anoption can be viewed as the probability ofan option being exercised. Generallyspeaking, an OTM option will have a delta ofclose to 0 (ie no chance), an ATM option willhave a delta close to 0.5 (ie 50/50 chance)and an ITM option, will tend to behave likethe underlying and will therefore have a deltaclose to one (ie every chance).

l How can the delta of an option be used?The delta of an option is a useful tool, since itallows a trader to hedge (ie cover) hisunderlying futures positions. For example,if he buys an option with a delta of 0.5, heknows that for every two of these options,this is like having one position in theunderlying. Similarly, a delta of 0.25 means aratio of 4:1 (ie a trader would need to do 4options to every one of the underlying).Knowing the delta of an option is thereforean important tool, in that it allows a trader toconstruct so-called ‘delta neutral’ positions.

l GammaThe gamma of an option is like a secondderivative, in that it measures:

the rate of change of the delta, given a oneunit change in the price of the underlying

Like the delta, the gamma is also influencedby the passage of time (time decay). Forexample, an ATM option close to expiry maystill have a very high gamma reflecting thepossibility that the option’s delta maysuddenly swing from 0 to 1.This is because,at expiry, the option will be either worthsomething, or nothing.

l ConclusionOptions are an important and effective riskmanagement tool.They can be used either asa stand alone product, or in conjunction withpositions in the underlying futures contractsthemselves.

The buyer of an option (whether a call or aput) is safe in the knowledge that they cannever lose more than the premium cost.Therisk profile is therefore said to be‘unlimited profit potential/limitedlosses’

The seller of an option however (whether acall or a put), assumed unlimited liability inreturn for collecting the option premium.Their risk profile is therefore the mirrorimage of the option buyer mentioned above,in that they have ‘limited profitpotential/unlimited losses’.


Mid-Curve STIR options were first introducedon 15 May 1998.They are currently available onthe following contracts:

l Three Month Euro (EURIBOR) FuturesContract

l Three Month Eurodollar Futures Contractl Three Month Sterling (Short Sterling)

Futures Contract

They are designed as an addition to the plainvanilla quarterly and serial options on STIRSmentioned above. However, unlike thesetraditional options, the Mid-Curve optionsdeliver into an underlying futures position onlonger dated contract months.

They are called “Mid-Curve” to distinguish themfrom the plain vanilla options, that deliver intowhat is generally regarded as the “short end” (ieup to one year) of the yield curve.

Definition of a Mid-Curve optionA Mid-Curve option can be viewed as a shortdated option which, on expiry, delivers into alonger dated futures contract.

For example, a one year Mid-Curve optiondelivers into an underlying three month “red”23

futures contract, ie expiring 12 months later.

Like Euronext.liffe’s STIR options, as previouslymentioned, Euronext.liffe’s Mid-Curve optionshave both:

l Quarterly expiry months; andl Serial expiry months.

However, the difference is that the Mid-Curveoptions expire one year before the underlyingfutures contract to which they relate.

l Quarterly expiry monthsThe underlying futures contract here is thesame quarterly futures contract month, butfor one year forward.

For example:The June ’05 quarterly Mid-Curve optioncontract, is an option on the June ’06EURIBOR futures contract, not the June ’05futures contract.

Hence the option will still expire on acertain date in June ’05.

However, if it is exercised, then the holder ofthe option will end up with a position in theJune ’06 futures contract (ie one yearforward).

l Serial expiry monthsThe underlying futures contract here is thenext quarterly futures contract month, butfor one year forward.

For example:The May ’05 serial Mid-Curve optioncontract is an option on the June ’06EURIBOR futures contract, not the June ’05futures contract.

Hence the option will still expire on acertain date in May ’05.

However, if it is exercised, then the holder ofthe option will end up with a position in theJune ’06 futures contract (ie the nextavailable quarterly futures contract, one yearforward).

l Contract months listedAt any one time, Euronext.liffe lists fourquarterly and two serial expiry months forits Mid-Curve options, such that the frontthree calendar months are always availablefor trading (see below).


One year Mid-Curve options l ll

23 Red months are defined as the fifth to eighth quarterly delivery contract months. So for example if the current front month issay June 05, thenJune ’06 would defined as “red Sep”.

11

The important thing to remember aboutMid-Curve options, is that they all are basedon a quarterly underlying futures contract,but for one year forward.

For example:If it is now the end of July ’05, then the menuof Mid-Curve options listed on theEURIBOR contract would be as follows:

l Strike price intervals The strike prices available for the Mid-Curveoptions are 0.125 intervals for the first fourquarterly and all serial delivery months forboth the Three Month Euro (EURIBOR) andThree Month Sterling (Short Sterling)Futures Contracts.

l Advantages of using Mid-Curve optionMid-Curve options can provide users with arange of instruments to efficiently tradeinterest rate volatility and changes in yieldcurve shifts, further out along the yieldcurve.

They also allow participants to manage suchlonger dated exposures at a lower cost thanthrough traditional options.This is becauseof the lower time premium associated withMid-Curve options. Equally they can alsoenable users to capture greater volatility andthereby offer more precise tradingopportunities/strategies than can beobtained using plain vanilla STIR options.

Mid-curve options have particular benefitsfor three types of users:

Market makers in Forward Rate Agreement(FRAs) – which are essentially OTC tailormade financial futures – Interest Rate Swapstraders and users of option related OTCinstruments.They also provide an additionalrisk management tool for Treasury Managersand arbitrageurs.


STIR Mid-Curve option expiry calendar

Mid-Curve option: Underlying future:

August ’05 (serial) Mid-Curve September ’06 Futures Contract

September ’05 (quarterly) Mid-Curve September ’06 Futures Contract

October ’05 (serial) Mid-Curve December ’06 Futures Contract

December ’05 (quarterly) Mid-Curve December ’06 Futures Contract

March ’06 (quarterly) Mid-Curve March ’07 Futures Contract

June ’06 (quarterly) Mid-Curve June ’07 Futures Contract


For more information about Euronext.liffe’s STIRproducts please contact:

Interest Rate Product Management:

tel +44(0)20 7379 2222fax +44 (0)20 7929 1050email [email protected] www.euronext.com

Contacts l ll

4216/Oct-05/1000/US

www.euronext.com

Amsterdam P.O. Box 19163 1000 GD Amsterdam The Netherlandstel +31 (0)20 550 44 44 fax +31 (0)20 550 49 00

Brussels Palais de la Bourse/Beurspaleis Place de la Bourse/Beursplein 1000 Brussels Belgiumtel +32 (0)2 509 12 11 fax +32 (0)2 509 12 12

LisbonAv. da Liberdade, Nº 196, 7º Piso1250-147 LisbonPortugaltel +351 21 790 00 00fax +351 21 795 20 26

LondonCannon Bridge House1 Cousin LaneLondon EC4R 3XXUnited Kingdomtel +44 (0)20 7623 0444fax +44 (0)20 7588 3624

Paris 39, rue Cambon 75039 Paris Cedex 01 Francetel +33 (0)1 49 27 10 00 fax +33 (0)1 49 27 14 33

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