Embed Size (px)
Citation preview
DERIVATIVES:DERIVATIVES:Concept , StructureConcept , Structure
& Valuation & Valuation
Contents of the presentation What are derivatives? Why are derivatives required? Types of Derivatives History of derivative markets Players in the derivative markets How derivative markets are organized? Valuation of Derivatives
Types of markets Cash: Payment is made as soon as the deal is struck
Tom:Price is decided today whereas the transaction will be settled on the next business day
Spot: Price is decided today whereas the transaction is settled two (or More) business days later
Forward/future: Price is decided today whereas the transaction takes place on a future date (few months)
Forward Vs Cash Transactions We might expects any transaction that settles today
to be a cash transaction and anything settling from tomorrow onward to be a Forward.
Unfortunately, this is not always the case and depending on the underlying financial asset, a cash transaction can range from today for a money market transaction to several weeks, or longer in some securities markets.
A forward transaction does not commence until the settlement day passes the cash settlement date.
Eg.In foreign exchange market, a Forward is a transaction that settles after two business days. In the Indian Equity market minimum Forward we can have is 8 days.
Derivative : What is it?
Derivative is a financial instrument whose value is derived from an underlying assets such as
Commodities Equity shares Equity share index Bonds Currencies
DERIVATIVES’ WORLD
FORWARD/FUTURE
SWAP
OPTION
Need for Derivatives Market.
The derivative market helps to transfer the risks from those who have them but may not like them to those who appetite for them.
Market RiskCredit Risk
Price Discovery.
Increased integration of national financial markets with the international markets.
Derivative market helps to increase savings and investment in the long run.
Types of Derivatives Exchange traded instruments :
Interest rate futures and options. Currency futures and option. Stock Index futures and option. Stock futures and option.
OTC Instruments: Forward rate agreements. Interest rate swaps Currency swaps
Forward A forward contract is a customized
contract between two entities, where settlements takes place on a specific date in the future at today’s pre-agreed price.
What is a Forward Rate Agreement (FRA) ? FRA is an off-balance sheet contract between two counter-parties to
exchange interest payments for a specified period starting in future – the interest payments are calculated on the notional principal– the specified period is from the start date to the maturity date – the floating rate is the actual rate on the start date of the swap and
available for the entire specified period
Convention of FRA : 3 X 6 month FRA, at 9.35% against 91-day T-Bill rate on a notional principal of Rs. 25 crores
– 3 X 6 implies specified period : start dates and maturity dates– Fixed rate payer pays 9.35% for 3 months from start date to the
maturity date– Floating Rate payer pays 91-day T-Bill rate which would be
determined on the start date of the swap– the net amount would be settled on the start date
Trade date Maturity dateStart Date
t=0 t+3m t+6mSpecified Period
OBJECTIVE Acorporate treasurer plans to borrow Rs.10 crore 6 months from now for 3 months. i.e. He will borrow in August and return it on NovemberRisk The interest rate will go upCurrent Interest rate for 3 months is 8% p.aFRA The treasure wants to hedge himself against rise in interest rates using 6X9 FRAMarket Quotations from a Bank for 6x9 FRA is 8.1% p.aTreasury Buys the 6x9 FRA at 8.1% p.aAfter 6 Months3 Months rate is 8.5%The bank compensate the firm for the difference in interest rates. Compensation= ((8.5-8.1)/100)x10 crs x 90/360=Rs.97,919The treasury invest this amount for 3 months at 8.5% Amount Received=(97919(1+0.085))/4= Rs.100,000Firm Borrows Rs.10crs for 3 months at 8.5%Rs.10 crs x (8.5/100)*(90/360)=Rs 21,25,000Net Cost of the firm is =2125000-100000=2025000The net interest rate is =(2025000/100000000)x(360/60)=8.1% p.a
3 Months rate is 7.5% The corporate compensate the bank for the difference in interest rates. Compensation= ((8.1-7.5)/100)x10 crs x 90/360=Rs.1,47,239The firm borrows this amount plus Rs.10 crs at 7.5% for 3 months The cost of total fund borrowed is= Rs.10crs x (7.5/100) x (90/360)=Rs.18,75,000Plus compensation amount= 147230 x (1+ 0.075)/4=150000Total cost of Firm= 1875000+150000= Rs.2025000The net interest rate is =(2025000/100000000)x(360/60)=8.1% p.a
FORWARD RATE AGREEMENT
Valuation of FRA (Pricing) Market 6 m deposit interest rates = 8.50 / 8.60
Market 9 m deposit interest rates = 8.70 / 8.80
Pricing 6 v 9 FRA
1. Borrow for 6m at 8.60%
2. Invest for 9m at 8.70%
Today 6m 9m +958,773 -1,000,000 - 958,773 +1,021,333 FRA bid rate = (21,333 / 1,000,000) * 4 *100 = 8.5331%
1. Invest for 6m at 8.50%
2. Borrow for 9m at 8.80%
Today 6m 9m
-959,233 +1,000,000 +959,233 -1,022,542 FRA offer rate =(22,542 / 1,000,000) * 4 * 100 = 9.0168%
Mechanics of a FRA
On the trade date, buyer and seller agree to exchange cash, on a specified future date, called the settlement date.
The basis for their exchange will be the prevailing interest rate on the settlement date, the reference rate that will be used is agreed upon today.
What is being traded today is the future interest rate; hence the name FRA
Mechanics of a FRA The buyer of the FRA expects
interest rates to go up; the seller expects the rate to fall.
On the settlement date, if the actual rate is higher than the agreed rate, seller pays the buyer.
On the settlement date, if the rate is lower, buyer pays the seller.
Terminology 2X5, 3X9 etc.
Future A future contract is an agreement
between two parties to buy or sell an underlying asset at a certain time in future at a certain price.
An Example of Hedging
A buyer faces many risks (price risk, liquidity risk, credit risk, operating risk) in equity investment.
Price risk is made of two parts: Price movement due to market sentimentsPrice movement due to company-specific factors
Say beta of Infosys is 1.5 Assume that Infosys equity is selling at Rs.4000 Say over a day, Infosys equity price moves to Rs. 3900 when the index
moves down by 1% Of this price movement of 100, market sentiment causes Rs.60. Remaining s.40 is due to company-specific factors
Continued…
•LLong ong StockStock, , SShort Index hort Index FuturesFutures
Suppose that a buyer does not want to assume
the price risk of Rs.60 due to market sentiments
Assume that the equity index future is selling at 2000. He will sell “n” index futures where “n” is calculated as follows:
n = (Price of the share*beta)/(value of the index)
In this case, n = (4000*1.5)/(2000)=3
If the index goes down by 1% to 1980 (that is, 20) as the seller he gains Rs.20*3= Rs.60
Continued..
LLong ong StockStock, , SShort Index hort Index FuturesFutures
Gain/loss when Index down by 1%, Infosys down by 1.5%
Short on Index 3 units: + 60
Long on Share 1 unit: -60
Buy Future : A Buy @ 5 @ B Sell
Long Future
-30
-20-10
010
2030
4050
6070
80
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Long Future
Short Future Position
Short Future
-80
-60
-40
-20
0
20
40
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Short Future
Futures contract are written on…
Livestock Foreign currency Stock index Shares Food grains Meat Petroleum Metals
Backwardation and Contango Contango is the situation when
FP>SP
Backwardation is the situation whenSP>FP
History of Forward market
12th century BC: China, Egypt, Austria, India and Japan used forward market.
During the Renaissance,Venetian spice traders , awaiting a cargo on the high seas , would enter into a forward contract,agreeing to a price for future delivery , while for 100 of years.
Japanese Rice Farmers have used futures market to secure the future value of their production.
Futures were used in a large measure in “Tulip Bulb Mania” of that Century.
“Forward Pricing”was regularized by CBOT in 1848 & Formal Future trading was established in 1865. (SHOCK)
Financial Future
Bretton Woods collapsed simultaneously Financial Future was born (1972-International Monetary Market -CME) (Currency Future) (SHOCK).
CBOT introduced Future based on GNMA in 1975.
IMM launched its Treasury Bill Future in 1976.(SHOCK)
CBOT started trading on Treasury Bond Future 1977.
1979-1980: Interest rate volatility- Interest Rate Future
INDEX FUTURE
1982-Commodity Future Trading Commission (CFTC) approved Index Future and KCBT was first to introduce it on Kansas City Value Line Index Future(KCVLIF) (24th February 1982).
Chicago Mercantile Exchange(CME) on S&P500 on April 1982.
NYFE on New-York Stock Exchange Composite Index(NYSCI) on May 1982.
CBOT on its own Future Index on August 1983.
S&P CNX Nifty FuturesContract SpecificationsSecurity descriptorThe security descriptor for the S&P CNX Nifty futures contracts is:Market type : NInstrument Type : FUTIDXUnderlying : NIFTYExpiry date : Date of contract expiry
Instrument type represents the instrument i.e. Futures on Index.Underlying symbol denotes the underlying index which is S&P CNX NiftyExpiry date identifies the date of expiry of the contract
Underlying InstrumentThe underlying index is S&P CNX NIFTY.
Trading cycleS&P CNX Nifty futures contracts have a maximum of 3-month trading cycle - the near month (one), the next month (two) and the far month (three). A new contract is introduced on the trading day following the expiry of the near month contract. The new contract will be introduced for a three month duration. This way, at any point in time, there will be 3 contracts available for trading in the market i.e., one near month, one mid month and one far month duration respectively.
Expiry dayS&P CNX Nifty futures contracts expire on the last Thursday of the expiry month. If the last Thursday is a trading holiday, the contracts expire on the previous trading day.
Trading ParametersContract sizeThe permitted lot size of S&P CNX Nifty futures contracts is 200 and multiples thereof
Price stepsThe price step in respect of S&P CNX Nifty futures contracts is Re.0.05.
Base PricesBase price of S&P CNX Nifty futures contracts on the first day of trading would be theoretical futures price.. The base price of the contracts on subsequent trading days would be the daily settlement price of the futures contracts.
FORWARD Vs FUTURE OTC in nature Customised contract
terms hence Less Liquid No Secondary market
No margin Payment Settlement happens
at end of period
Trade on an organised exchange
Standardised contract terms hence More liquid Secondary market
Requires margin requirement
Follows daily settlement
Future Strategies
Hedging Long Stock, Short Index Futures Short Stock, Long Index Futures Have portfolio,Short Index Futures
Speculation Bullish Index,Long Index Futures Bearish Index, Short Index Futures
Options An option is a contract.
It gives one party (the holder of the option) the right to choose, during a specified period of time, to buy (or sell, respectively) a specified quantity of a specified asset (for instance a stock) at a given price.
The other contract party (the writer of the option) has the obligation to fulfill the holder's right.
History of Options market
The idea of option is ancient. The Romans wrote options on the cargoes
that were transported by their ships. In the 17th Century there were active options market in Holland.
Options were used in a large measure in “Tulip Bulb Mania” of that Century.
Options were traded in the USA & UK during the 19th Century in agricultural commodities . Earlier to this it was declared illegal.
In 1973 Black and Scholes published a seminal paper on Option pricing.
History of options market
Pre 1973: PUTs and CALLs traded on OTC 1973: CBOE listed call option on 16 equity
shares; introduces the market-maker system; starts a clearing corporation
NYFE -1980 LIFFE-1982 Singapore Monetary Exchange(SIMEX)-1983 1982: CBOE introduces index options
Assets on which options can be written… Shares Share index Treasury bills Treasury notes Treasury bonds Foreign currency Future contracts
Life of an option
The life of an option is limited: it has an expiration date. After the expiration date all the rights and obligations conferred by the option are null and void. The option holder can exercise the option, i.e. declare he or she wants to use the right to buy (or to sell) conferred by the option.
Options Options are of two types –Calls and Puts Call options give the buyer the right but not the obligation
to buy a given quantity of the underlying asset , at a given price on or before a given future date.
Put options give the buyer the right , but not the obligation to sell a given quantity of the underlying asset at a given price on or before a given date.
• Long=Buy= Holder• Short=Sell=Writer• C= Current Price of the Call• E=Exercise Price=Strike Price• So=The current price of the share• S1=The stock price at the expiration date of the call.
CALL OPTIONA Call Option is an option to buy a stock at a specific price on or before a certain date. In this way, Call options are like security deposits. If, for example, you wanted to rent a certain property, and left a security deposit for it, the money would be used to insure that you could, in fact, rent that property at the price agreed upon when you returned. If you never returned, you would give up your security deposit, but you would have no other liability. Call options usually increase in value as the value of the underlying instrument increases.
PERCEPTION: PRICE WILL RISE BUYS CALL@ RS.4 OF STRIKE
PRICE=RS.140Price Price Exercise
90 140 -495 140 -4
120 140 -4140 140 -4150 140 6155 140 11160 140 16
Profit/Loss for selected share values: Long Stock Short Call
Call OptionsCall Options
Long Call Positions
Buy=Long=Hold Call
-10
0
10
20
30
40
50
60
70
Buy Call
PUT OPTIONS Put Options are options to sell a stock at a specific price on
or before a certain date. In this way, Put options are like insurance policies If you buy a new car, and then buy auto insurance on the car, you pay a premium and are, hence, protected if the asset is damaged in an accident. If this happens, you can use your policy to regain the insured value of the car. In this way, the put option gains in value as the value of the underlying instrument decreases.
If all goes well and the insurance is not needed, the insurance company keeps your premium in return for taking on the risk.
Long Put Options
PERCEPTION: PRICE WILL FALL BUYS PUT@ RS.16 OF STRIKE
PRICE=RS.14070 140 5480 140 4490 140 34
140 140 -16150 140 -26160 140 -36170 140 -46180 140 -56
Profit/Loss for selected share values: Short Stock Long Call
Long Put Positions
Buy=Long=Holder Put
-10
-5
0
5
10
15
20
Buy Put
Market Price
Strike Prices Strike Prices
166 168 170 172164162160
In the Money Call Options
Out of the Money Call Options
Out the Money Put Options
In the Money Put Options
CallsCalls
PutsPuts
STOCK OPTIONSContract Specifications
Security descriptorThe security descriptor for the options contracts is:Market type : NInstrument Type : OPTSTKUnderlying : Symbol of underlying securityExpiry date : Date of contract expiryOption Type : CA / PAStrike Price: Strike price for the contract Trading cycleOptions contracts have a maximum of 3-month trading cycle - the near month (one), the next month (two) and the far month (three). The new contracts are introduced for three month duration.Expiry dayOptions contracts expire on the last Thursday of the expiry month. If the last Thursday is a trading holiday, the contracts expire on the previous trading day.Strike Price IntervalsThe Exchange provides a minimum of five strike prices for every option type (i.e. call & put) during the trading month. At any time, there are two contracts in-the-money (ITM), two contracts out-of-the-money (OTM) and one contract at-the-money (ATM).
INDEX OPTIONContract Specifications
Security descriptorThe security descriptor for the S&P CNX Nifty options/BSE 30 contracts is:
Market type : NInstrument Type : OPTIDXUnderlying : NIFTY/BSE 30Expiry date : Date of contract expiryOption Type : CE/ PEStrike Price: Strike price for the contractTrading cycleIndex options contracts have a maximum of 3-month trading cycle - the near month (one), the next month (two) and the far month (three). The new contracts are introduced for three month duration.Expiry dayIndex options contracts expire on the last Thursday of the expiry month. If the last Thursday is a trading holiday, the contracts expire on the previous trading day.Strke Price IntervalsThe Exchange provides a minimum of five strike prices for every option type (i.e. call & put) during the trading month. At any time, there are two contracts in-the-money (ITM), two contracts out-of-the-money (OTM) and one contract at-the-money (ATM). The strike price interval is 10.
EXOTIC OPTIONS Range Forward Contract or Cylinder
Option: Short Cylinder option: Long Put at X1 and Short
Call at X2 where (X2>X1). The logic:It guarantees that the underlying
asset can be sold for a price between X1 and X2 at the maturity of the options.
Long Cylinder option: Short Put at X1 and Long Call at X2 where (X2>X1).
The logic:It guarantees that the underlying asset can be purchased for a price between X1 and X2 at the maturity of the options.
The price of the call is equal to the price of Put. What will happen if X1=X2?
TRADE DATE 11-Apr-02STOCK S&P CNX NIFTYSPOT PRICE (11/04/2002)* 1133MATURITY DATE OF OPTIONS 25-Apr-02STRATEGY BUY S&P CNX NIFTY
BUY PUTSELL CALL
* Note Average of the Day
ParticularsMarket Price Fair value$ Market Price Fair value$
Put - Strike price (Bought) 1160.00 1160.00 1150.00 1150.00Put - Premium 28.93 32.74 13.00 12.48Call - Strike price (Sold) 1160.00 1160.00 1200.00 1200.00Call - Premium 6.67 9.12 1.00 2.20GAP=(Put -Spot)-(Put Premium-Call Premium) 4.74 3.38 5.00 6.72On maturity, market position:Below the bought price(1120) Absolute Return 4.74 3.38 5.00 6.72
Annual Return 10.76% 7.67% 11.35% 15.25%At bought price (1133)Absolute Return 4.74 3.38 5.00 6.72
Annual Return 10.76% 7.67% 11.35% 15.25%Between bought and strike price (1133-1160) 4.74 3.38 NA NA
Annual Return 10.76% 7.67% NA NABetween Put and call strike price (1160-1160) 4.74 3.38 NA NA
Annual Return 10.76% 7.67% NA NAAt strike price(1160) Absolute Return 4.74 3.38 NA NA
Annual Return 10.76% 7.67% NA NAAbove strike price(1180) Absolute Return 4.74 3.38 NA NA
Annual Return 10.76% 7.67% NA NABetween bought and strike price (1133-1150) NA NA 5.00 6.72
Annual Return NA NA 11.35% 15.25%Between Put and call strike price (1150-1200) NA NA
Minimum Return NA NA 5.00 6.72Annual Return NA NA 11.35% 15.25%
Maximum Return NA NA 55.00 56.72Annual Return NA NA 124.83% 128.73%
Above strike price(1210) Absolute Return NA NA 55.00 56.72Annual Return NA NA 124.83% 128.73%
$ Note Fair Value is calculated based Black and Scholes Model
Product I (Capital assured) Product II (Assured with upside potential)
TRADE DETAILS
ANALYSIS OF RETURNS UNDER DIFFERENT MARKET CONDITIONS
Short future positionShort future position
-80
-70
-60
-50
-40
-30
-20
-10
0
10
20
30
Sell Call Buy Put Short Future
Non-Standard American Options In Standard American option , exercise can take
place at any time during the life of the option and the exercise price is always the same.
Bermudan Option(AO) is a OTC product on Bond which can be exercised only on coupon payment dates.
Warrant can be exercised during only part of its life and sometimes the strike price increases with the passage of time.
7- Year warrants: Exercise Period after 3 years. Strike Price Rs.30 During 3 to 4 Years Rs.32 During 5 to 6 Years Rs.33 During 7 Years
Forward Start Options are options that will start at some time in Future.
ESOPs refers to various schemes of offering an equity stake by a Company to its employees. The stake may be in various forms such as allotment of shares, grant of stock options that entitle the employee to acquire shares in the future, or simply by way of rewarding an employee based on the appreciation in the value of the shares.
Forward Start Options
Chooser Options A chooser options has the feature that , after a
specified period of time, the holder can choose whether the option is a call or a put.
If the options underlying the chooser option are both European and have the same strike price , put-call parity can be used to provide a valuation formulla.
FUTURES OPTIONS•Options on Future Contracts.
–Options on Interest Rate Futures
–Option on Eurodollar futures.
Put-Call Parity Portfolio P1: One European call option Cash for an amount of Ee-rt
Portfolio P2: One European Put Option One Share of stock worth So
COST= C+ Ee-rt=P+So
Portfolio Investment(Outflow) If S1>E If S1<=E
P1Call C S1-E 0Cash Ee^-rt E E
Total S1 EP2 Put P 0 E-S1One Share So S1 S1
Total S1 E
Value at Expiration date
Spot Price=Rs.50 Exercise Price=Rs.48 Risk free return =10% p.a 3-month European Call=Rs.6 3-month European Put=Rs.4 P1= C+ Ee-rt =6 +48e-(0.10 * 3/12) = 52.81 e=2.7183 P2 = P+So = 4+50=55 P2>P1 Buy a call and Short Put and stock. Cash Flow= -6+4+50=48 Risk Free return for 3 months= 48e(0.10 * 3/12) =49.21 After Three months if Spot is greater than Rs.48 call will be
exercised and if it less then put (counter-party) will be exercised .In either case the investor will end up buying the stock for Rs,48.
The net profit is Rs.49.21- Rs.48= Rs.1.21
Binary Options Binary options are options with discontinuous
payoffs. Cash-or-Nothing Call: This pays off nothing if the
stock price ends up below the strike price at time T and pays a fixed amount ,Q, if it ends up above the strike price.
Asset or Nothing Call:This pays off nothing if the stock price ends up below the strike price and pays an amount equal to the stock price itself if it ends up above the strike price.
Asian options are options where payoff depends on the average price of the underlying asset during at least some part of the life of the option. C=Max(0,S(ave)-X)
Asian Options
Barrier Options Barrier options are options where the
payoff depends on whether the underlying asset’s price reaches a certain level during certain period of time.
Call Cap: It is exercised automatically on a day when the index reaches a barrier equal to the strike price plus Rs.30.
Put Cap:It is exercised automatically on a day when the index reaches a barrier equal to the strike price minus Rs.30.
Global Futures & Options Volume
Global Futures & Options Volume
Call Put
CallPut
Buy SellBullish
Bearish
Swap Swaps are private agreements between two
parties to exchange cash flows in the future according to a prearranged formula.
Interest Rate Swap: These entail swapping only the interest related cash flows between the parties in the same currencies.
Currency Swap:These entail swapping both principal and interest between the parties, with cashflows in one direction being in a different currency than those in the opposite directions.
Interest Rate SwapEXAMPLESITUATION Existing Borrower on Floating rates
For 3 Years, Interest Payable semi- annually based on 6 month LIBOR
VIEW Interest rates will rise
AIM To avoid the risk from increase in the interest rates
STRATEGY Enter into an Interest Rate Swap agreement with the Bank to
receive Floating Rate in exchange for paying Fixed Rate
Interest Rate Swap
LENDER
BORROWER BANK
Receives FloatingRate
Pays Fixed RatePays Floating Rate
The Borrower has hedged his loan effectively, servicing it on a Fixed Rate Basis.
IRS
Asset LiabilitiesFixed Floating
Fixed Floating
Payment Floating Interest on Liabilities Receipts Floating Interest on assets Net Payment=Fixed InterestFixed Interest through Swap Floating Interest through swap Net Receipt= Floating Interest
Interest Rate Swap (IRS)Anticipation Interest Rate Rise
Borrower
SWAPCounterparty
Asset LiabilitiesFloating Fixed
Floating Fixed
Payment Floating Interest on Liabilities Receipts Floating Interest on assets Net Payment=Floating InterestFixed Interest through Swap Fixed Interest through swap Net Receipt=Fixed Interest
Interest Rate Swap (IRS)Anticipation Interest Rate Fall
BANK
SWAPCounterparty
Receives floating
Swap market maker
Pays fixed Receives fixed
Pays floating
What is an Interest Rate Swap (IRS) ? IRS is an off-balance sheet contract between two
counterparties to exchange interest payments on specified date(s) over a specified period
One counterparty pays a fixed or floating rate of interest (fixed rate payer) on one basis, in return for a floating rate of interest (floating rate payer)
Floating rate could be any benchmark rate like MIBOR, T- Bill yield,Bank/FI PLR, CP Rate, bank rate etc.
Interest payments are calculated on a Notional Principal amount
Principal amount is not exchanged, but the net interest amounts (the difference between the two legs) are settled between the counterparties on the settlement date(s) of the contract
Bank
Receives FixedPays Fixed
Elements of a typical IRS Notional Principal
– the fixed and floating interest rate is calculated on a notional principal amount
– there is no actual exchange of principal
Fixed rate– predetermined rate, valid for the entire life of the
Swap
Floating rate– linked to a benchmark rate, keeps changing
periodically or on reset dates
Payment dates and conventions– swap start date, payment frequency, reset date,
maturity date
Documentation– ISDA - master agreement and schedule– ISDA-International Swap and Derivative Association.
Criteria for selecting a floating rate
benchmark
Available for the tenure of the swap
Transparency - Market determined rate & easily available
Relevant to the counterparties
Benchmark rate should be liquid and deep
Possible floating rate benchmarks in Indian markets– Treasury/Govt. Securities yields– Bank Rate– Bank deposit / lending rates (PLR)– CP Rate– Overnight Rates : NSE/Reuter’s Mibor
Overnight Index Swaps (OIS) Overnight rate is likely to be the most relevant
and acceptable floating rate benchmark
Overnight markets are deep and liquid - Average daily volumes of Rs. 16,000 crores
Most participants have significant exposure on overnight rate
Determination of overnight index would be relatively simple
Benchmark Overnight Rates :– NSE Mibid / Mibor (NSE 9:00 AM Rate) – Forex Premia
OIS : Example Bank A pays 7 days OIS at 9.25% for Rs.25 crores,
receives overnight rate, trade date : 18/9/2001
Details of the swap :– Notional Principal = Rs. 25 crores– Start date = 18.9.01– Maturity date = 24.9.01
Overnight index for 7 days :18.9 (Tuesday) 8.5%19.9 (Wed) 8.75%20.9 (Thursday) 8.4%21.9 (Friday) 8.65%22.9 (Saturday) 9.00%23.9 (Sunday) -24.9 (Monday) 8.25%
Cash flows of the OIS swap - explained
Notional principal 2500 LacsDuration of swap 7 daysFixed rate 9.25%Value date September 17, 1999Start date September 18, 1999
Actual callOpening principal Interest
Closing principal
September 18, 1999 8.50% 2500.00 0.58 2500.58September 19, 1999 8.75% 2500.58 0.60 2501.18September 20, 1999 8.40% 2501.18 0.58 2501.76September 21, 1999 8.65% 2501.76 0.59 2502.35September 22, 1999 9.00% 2502.35 1.23 2503.58September 23, 1999September 24, 1999 8.25% 2503.58 0.57 2504.15
Interest on the floating leg +2504.15-2500 4.150057 lacsInterest on the fixed leg +2500*9.25%/365*7 4.434932 lacs
Net interest payable 0.28487 lacs
( Rs in Lacs )
OIS : Example
Interest Accrued on floating leg =(1+8.5%*1/365)*(1+8.75%*1/365)*(1+8.4%*1/365)* (1+8.65%*1/365)*(1+9%*2/365)*(1+8.25%*1/365)* 25 crores - 25crores = Rs. 415005.73
Interest on Fixed leg = 9.25%*7/365 * 25 crores = Rs. 443493.20
Net payment to be made by bank A = Rs.443493.2 - Rs.415005.73 = Rs.28487.42
FRAs vs. IRS FRA is a forward starting Swap. The difference
between FRA & IRS :– Settlement Date
* in a typical swap the settlement happens at maturitySettlement Date = Maturity Date
* in a FRA the net payment is discounted to the swap start / settlement dateSettlement Date = Start Date
Floating Leg :– in a swap, the floating leg could have multiple resets– in a FRA, the floating is reset only once on the start
date of the swap and is available for the entire specified period of the swap
Interest Rate Swap Applications
LIABILITY MANAGEMENT
Floating Rate Liability in periods of Rising Interest Rates
(P)Fix the interest rates in view of expected rise
Fixed Rate Liability in periods of Falling Interest Rate
(P)Float the interest rates in view of expected decline
ASSET MANAGEMENT
Fixed Rate Asset in periods of Rising Interest Rates
(R) Float in view of expected rise
Floating Rate Asset in periods of Falling Interest Rate
(R ) Fix in view of expected decline
CREDIT SWAP
Credit swap reduce credit risk through diversification.
The most common credit swap is called a total rate of return swap(TRORS).
Payer of TROR
Receiver of TROR
Total Rate of Return
LIBOR + Spread
Reference Asset
Total Rate of Return
Total Return= Interest Flows + (Final Value –Original Value)
CREDIT SWAP The total rate of return payer id the legal
owner of the reference asset. For the period of the transaction, the total
rate of return payer has created a short position in the market risk and a short position in the credit risk of the reference asset.
The total rate of return receiver is not legal owner of the reference asset.
For the period of transaction only, the total rate of return receiver has a synthetic long position in the market risk and a synthetic long position in the credit risk.
CREDIT SWAP At the maturity of the transaction , the total rate of return receiver
may choose, but is not obliged , to purchase the reference asset at the then prevailing market price.
In the event of default of the reference asset prior to the maturity date of the TRORS, the TRORS usually terminates.
If the TRORS terminates due to a default, the total rate of return receiver makes the total rate of return payer “whole” for the market risk and credit risk of the reference asset.
The the total rate of return receiver may make a net payment of the difference between the price of the reference security at the beginning of the transaction and the price of the reference security at the time of default.
Alternatively , he may agree to take delivery of the defaulted reference asset and pay the initial price of the reference asset to the total rate of return payer.
Once this has occurred, neither the payer nor the receiver has any additional obligation to the other party &TRORS terminates.
CREDIT SWAP TRORS are simply another form of
financing. TRORS are off-balance sheet transactions. A TRORS is a bilateral financial contract
between a total-return payer and total return receiver.
TRORS have been around since at least 1987.
Credit Default Swaps & Option A credit default swap or option is simply an
exchange of a fee in exchange for a payment if a credit default event occurs.
Credit default swaps differ from TRORS in that the investors does not take the price risk of the reference asset, only the risk of default.
The investor makes no payment unless a credit default event occurs.
If the fee is paid up front the agreement is likely to be called a credit default option.
If the fee is paid over time the agreement is more likely to be called a credit default swap.
CREDIT DEFAULT SWAP Seller receives a fee in return for
making a Contingent Payment if a predefined Credit Event occurs to the Reference Asset.
Underlying exposure can be single credits or basket of credit, or indices.Protection Buyer
Protection Seller
Option Premium
Contingent Payment upon an Event of Default of Reference Assets
Reference Asset
Derivative markets: India Active commodity futures market existed
prior to 1960s They were blamed for price volatility and
closed 1996: Sodhani Committee favours forward
market in financial instruments 1997: L.C.Gupta Committee favours
commodity future exchanges
Financial Futures Trading in India
Securities Law amended in December, 1999.
Bye-laws by SEBI in April, 2000. SEBI approves derivatives trading on 25th
May, 2000. S&P CNX Nifty Index Futures commenced
on NSE on 12th June, 2000. BSE launches BSE-30 Index Futures on
25th September, 2000. 2nd July 2001 Stock options were
introduced
Derivative market organization There are sellers and buyers of contracts 2-tier membership (trading member and
clearing member) A contract can be closed out in two ways:
prior to the expiry date: enter an off-setting contract
on the expiry date: cash or delivery Contract specified by the exchange
Derivative market organization.. Fully automated screen-based trade
in the derivative segment Anonymous order-driven market Different kinds of orders as in the
equity segment Trading user has access to: order
entry and order management
Derivative market organization.. Clearing user: monitoring the trading
user and managing risks by setting trader’s limits
Brokerage charges maximum 2.5% (exclusive of statutory levies)
Transaction charges 0.002% each side
NSCCL is the clearing agent in NSE
Derivative market organization.. Membership eligibility is based on
net worth and security deposits Open positions are marked-to-
market on daily basis Settlement on T+1 basis
Valuation of Derivatives
Pricing a SWAP Pricing of Future Pricing of Option
VALUE Vs PRICE
We can use theoretical method to determine the value of an derivative product
In this context value has a very precise meaning , it is what the contract is intrinsically worth.
This is sometimes different to the price of the option which is what actually pays for it.
Valuation of Interest Rate Swaps (Constructing the curve)
Valuation curve to be used should be the Implied forward
rates derived from the Zero coupon curve (so as to remove
the reinvestment risk). Appropriate Credit Risk spread
should be added to factor the same in the pricing /
valuation.
As Zero securities for every tenor may not be available,
we would have to construct a zero curve from the Par rates
(coupon securities yields etc.). This process is known a
“Bootstrapping”.
The Derivation of Zero & Implied forwards rates is as
follows:
Years Par rates % Zero Rates % Implied Forward Rates %
1 5.0000 5.0000 5.0000
2 5.1100 5.1128 5.2257
3 5.3000 5.3122 5.7122
4 5.4700 5.4940 6.0414
Given the Par rates, the zero rates are derived as follows:
Year 2 => 100 = 5.11 + 105.11
1.05 (1+ R2)^2
R2 = 5.1128%
Year 3 => 100 = 5.30 + 5.30 + 105.30
1.05 (1.051128)^2 (1 + R3)^3
R3 = 5.3122%
Valuation of Interest Rate Swaps (Constructing the curve continued)
Year 4 => 100 = 5.47 + 5.47 + 5.47 + 105.47 1.05 (1.051128)^2 (1.053122)^3 (1 + R4)^4
R4 = 5.4940%
Now having derived the zero rates we derive the Implied forward rates:
Year 2 => (1 + R2) = (1.051228)^2 R2 = 5.2257%
(1.050000)^1
Year 3 => (1 + R3) = (1.053122)^3 R3 = 5.7122%
(1.051128)^2
Year 4 => (1 + R4) = (1.054940)^4 R4 = 6.0414%
(1.053122)^3
Valuation of Interest Rate Swaps (Constructing the curve continued)
Hence, the Fixed rate implied by the curve is 5.47%.
Say we have entered into a 4 year IRS for a Notional Principal of INR 1,000,000 wherein we receive Fixed at 5.47% and pay Floating and after 1 year (I.e. the Swap has a residual life of 3 years) the Par rates have moved as follows:
Years Par rates %
1 5.02
2 5.27
3 5.32
The Swap value would be as follows:
Price for Forward and Futures
The cost of CARRY model: Forward(or Futures)=(Spot Price+Carry
Cost-Carry Return)• F=S0+CC-CR
Spot Price = Current Price Carry Cost = Holding Cost, Interest
Charges on Borrowing.- Insurance,Storage Costs etc.
Carry Return= Dividends
Pricing of Future Contract
Case1- Securities Providing No Income
•F=S0ert
•S0=Spot Price•r=Risk Free Return•t=time to maturity•Example:•Spot Price of Non-payable dividend XYZ
Share=Rs.70,•Contract matures after 3months.•Risk-free return=8% (For 3 months)•e=2.7183•F=70e(0.25)(0.08)
• =70x1.0202• = Rs71.41
Pricing of Future Contract
Case2- Securities Providing a known cash Income• F=(S0-I)ert
• S0=Spot Price
• r=Risk Free Return• t=time to maturity• I=Present Value of the Income• Example:• Spot Price of dividend payable XYZ Share=Rs.38,• Contract matures after 6months.• Contract size=100 shares• Risk-free return=10% (For 6 months)• Dividend=Rs.1.50 per share after 4 months• Present Value of the Dividend I= (100x1.50)e-(4/12)(0.10)=Rs.145.08• F=(3800-145.08)e(0.5)(0.10)
• =3654.92 x 1.05127• =Rs3842.31
Pricing of Future Contract
Case3- Stock Index Futures• F=(S0-I)ert
• S0=Spot Price
• r=Risk Free Return• t=time to maturity• I=Present Value of the Income• Example:• Two month futures contract on NIFTY• Let us assume that M&M will be declaring a dividend of Rs.10
per share after 15 days of purchasing the contract.• Current Value of NIFTY=1200 r=15%• Multiplier =200 200x1200=240,000• If M&M has a weight of 7% in NIFTY,its value in NIFTY is
Rs.16,800 i.e(240,000 x 7/100).• If the market price of M&M is Rs.140, then a traded unit of
NIFTY involves 120 shares of M&M.• Present Value of the Dividend I= (120x10)e-(15/365)(0.1398)
• e=2.7183• F=Rs.1221.80
Premium
PREMIUM (OR OPTION PRICE)= INTRINSIC VALUE + TIME VALUE
INTRINSIC VALUE
For a call option:Intrinsic value = Price of the underlying - Exercise price
For a put option: Intrinsic value = Exercise price - Price of the underlying
Intrinsic value can never be negative
TIME VALUE
Time Value=Premium - Intrinsic Value
Basically three factors influence the time value:
The time to maturity The interest rate The volatility of the underlying asset
FACTORS AFFECTING PREMIA
There are five major factors affecting the Option premium:
Price of Underlying Exercise Price Time to Maturity Volatility of the Underlying
And two less important factors: Short-Term Interest Rates Dividends
VOLATILITY
If you trade stocks, you are already familiar with Volatility. In the stock trader's world, it is known as risk. The larger the price fluctuations, the riskier the stock, and the more expensive the options for that stock.
If XYZ stock, currently at $50, has a volatility of 16%, that would imply that it is expected to trade in the range up or down of $42-$58. You should be aware that lower volatilities mean less movement in the stock price, while higher volatilities mean more movement in the stock price.
Valuation of Options
Re-defining option: One sided Future Contract. The buyer of an option gets best of both the worlds, protected if the price rises but benefiting if the price falls. A-Symmetric.
The value of option at Expiry: Call= Maximum (0, S0-E) Put = Maximum (0, E -S0)
Option Premium=Intrinsic Value+ Time Value Intrinsic Value=The difference between forward price and
the exercise price. Time Value= A part of price arising from the possibility that
the underlying price might move further in-the-money over the remaining life of the option.
Option Pricing Problem
Since the expected Forward Value is unknown when the option is executed, we need to model the likely Forward value outcomes of the option in order to derive the expected forward value.
Option Pricing Problem: Estimating Price movements in uncertainty.
Uncertainty:It is defined as the fact that we do not know what the price of the underlying instrument will be on the option expiry date. Cont.
–Expected Forward Value= E(Max(0, S0-E))>=0
–Option Premium=PV(E(Max(0, S0-E))>=0
Option Pricing Problem
In order to develop option pricing models, we need to be able to make some assumptions regarding the nature of the distribution of the underlying instrument price.
Distribution of this uncertainty(Price of underlying asset ) is that the movement in the underlying price is random, but that its potential range of outcomes can be defined with specific probabilities.
The Requirements of an Option Pricing Model
Determine a range of possible underlying prices at option expiry.
Assign probabilities to each price outcome.
Using these prices and probabilities, determine the expected value of these outcomes.
Calculate the present value of the expected value.
The Black and Scholes model uses a similar calculation method. The difference comes from the number of possible stock values: it is not a fixed set but a continuous interval. The stock can take any value from zero to infinity.
Obviously, not all the possible values have the same probability. The Black and Scholes model uses a "lognormal" probability distribution.
. We will now look at a graphical example illustrating the
calculation method and how the shape of the probability distribution affects the option's fair value.
The first distribution (green line) is used for the calculation of the fair value of a call with a strike of 40 and an underlying currently at 45.
Which of the two other distributions corresponds to an underlying currently at 35 .a) The flat, yellow, curve b) The pink, left shifted curve Yes. The curve (b) has the same dispersion as the original one, but it is centered around an underlying value of 35. Each possible value of the current underlying has a corresponding probability distribution function for the underlying value at the expiration date of the option
. If this distribution were exactly known, no simplification in terms of
using a model would have to made: the calculation of an option premium would be based a calculation based on facts.
It is therefore easy to understand that the most important problem for option pricing is to find an acceptable prediction method for these probability distributions.
The Black and Scholes model uses a method for the description of the underlying price movements commonly known as the random walk theory.
THE BLACK AND SCHOLES MODEL The Formula:
C=S0N(d1)- Ee-rtN(d2) Where C=Current Value of the option. t=Time remaining
before the expiration date r=Continuously compounded risk free rate of return. S0=Current price of the stock. E=Exercise price of the option = Standard Deviation of the continuously
compounded annual rate of return N(d1)=Value of the cumulative normal distribution
evaluated at d ttrESd /))5.0()/(ln( 2
011
ttrESd /))5.0()/(ln( 2
02
Valuation of Options Price of the option are influenced
by the following factors: Price of underlying security. Volatility. Length of time to expiration Interest Rates. Tax rules Margin requirements in case of
uncovered option writers. Transaction cost.
Valuation of OptionsInfluences on Option Value
Parameter Call Put
Price + -
Exercise price - +
Volatility + +
Time - -
Interest rates + -
Dividends - +
+ = Positive relationship - = Negative relationship
Delta: Hedge Ratio. This refers to the amount by which the price of an option changes for a unit change in the price of the underlying stock or index. BS= N(d1)
Gamma: The gamma represents the amount by which an option’s delta would move in response to a unit change in the underlying stock price or index. BS = z(d1)/S0 t
Theta: Theta represents the price decay that affects an option as it ages and loses time value.
Cont
GREEK
2/)( 2/2dedz
Rho: The rho measures the sensitivity of an option value to interest rates.
Vega: Vega measures the rate of change of the value of an option with respect to the volatility of the underlying asset.
)( 2dNeEtSB rt
dS tBS10
RATIOS
CLEARING AND SETTLEMENTCLEARING AND SETTLEMENT
Understanding volume
They benchmark the degree of activity Volume is the velocity of trading or
number of contracts traded in a day (and not the sum of buyers & sellers) .
To determine volume, simply add either all buyers or all sellers.
Number of contract traded includes creation of new contract, transfer or liquidation of a contract.
Understanding Open Interest
Open Interest (OI) measures the number of contracts held at the conclusion of a trading session
It is a description of participation -traders show their conviction to the market participation by taking their positions “home” with them, at least overnight.
Important as many transactions may take place during the day without initiating new contracts
An exampleDay 1 Trader A buys one
contract Trader B sells one contract Trader C buys one contract Trader D sells one contract
OI - 4 contracts Vol. - 2 contract
Day 2 Trader E buys one contract Trader A sells to offset
OI - 4 contracts Vol. - 1 contractDay 3 Trader F buys one
contract Trader G sells one contract Trader B buys to offset Trader C sells to offset Trader E sells to offset Trader D buys to offset
OI - 2 contracts Vol. - 3 contracts
MARGIN
Initial Margin:The amount that must be deposited in the margin account at the time a futures contract is first entered into is known as initial margin.
Maintenance Margin:This is somewhat lower than initial margin. This is set to ensure that the balance in the margin account never becomes negative.
Marking-to-Market:In the futures market, at the end of each trading day , the margin account is adjusted to reflect the investor’s gain/loss depending upon the future closing price. This is called marking-to-market.
Margin: Margin can be paid in terms of cash , bank guarantee or other acceptable collateral.
INITIAL MARGIN
Value at Risk (VAR): VAR methodology seeks to measure the amount of value that a portfolio may stand to lose within a certain horizon time period (one day for the clearing corporation) due to potential changes in the underlying asset market price.
The computation of initial margin on the futures market is done using the concept of VAR.
The initial margin amount is large enough to cover a one-day loss that can be encountered on 99% of the days.
For Trading Member , initial margin is calculated on the basis of net outstanding position of a trading member and gross outstanding position of all clients of the Trading Member.
INITIAL MARGIN Brokers are required to collect initial
margin up-front for all the open positions for all clients based on the margins compute by NSE/BSE SPAN (Standard Portfolio Analysis of Risk).
Initial Margin has 3 components SPAN Margin Premium Margin Assignment Margin
INITIAL MARGIN
Trading Member “ XYZ” trades in F&O segment for his two clients.
Member L(Position) S(Position) O(position) Client A 400 200 200 Client B 600 200 400 Total of TM 1000 400 600 VAR % Calculated for the day by NSCCL is
5%.
INITIAL MARGIN Client A:Initial margin of 5% will be levied
on 200*1000(Latest Traded Price) =2,00,000*5%=Rs10,000
Client B: initial margin of 5% will be levied on 400*1000(Latest Traded Price) =4,00,000*5% =Rs20,000
Total Initial Margin for XYZ = Long initial margin + Short initial margin = Rs10,000+ Rs20,000=Rs.30,000.
MINIMUM MARGIN Index Future=5% Stock Future=7.5% Short Index Option =3%
Mark to MarketNo of Units =100 XYZ Initial Margin= Rs.6000
Starting Date =2nd September Maintenance Margin=Rs.4500
Expiry Date= 21th September Current Future Price =Rs.900
Trading Day Future Daily Cumulative Margin Margin September Price(Rs)Gain/(Loss) Gain/(Loss) Account Call
Balance2 600.00 6000.00
598.20 -180.00 -180.00 5820.003 593.60 -460.00 -640.00 5360.004 594.00 40.00 -600.00 5400.005 589.50 -450.00 -1050.00 4950.006 584.80 -470.00 -1520.00 4480.00 15207 582.20 -260.00 -1780.00 5740.008 583.70 150.00 -1630.00 5890.009 577.30 -640.00 -2270.00 5250.00
10 577.10 -20.00 -2290.00 5230.0011 572.40 -470.00 -2760.00 4760.0012 570.10 -230.00 -2990.00 4530.0013 568.50 -160.00 -3150.00 4370.00 163014 569.80 130.00 -3020.00 6130.0015 573.80 400.00 -2620.00 6530.0016 573.60 -20.00 -2640.00 6510.0017 577.30 370.00 -2270.00 6880.0018 576.80 -50.00 -2320.00 6830.0019 578.80 200.00 -2120.00 7030.0020 578.00 -80.00 -2200.00 6950.0021 584.20 620.00 -1580.00 7570.00
Marking to Market for the XYZ Futures Contract
Mark to Market
The daily mark-to-market settlement price is the closing price of the respective product.
It is computed on the basis of the last half-an hour weighted average price of such contract in the F&O segment.
In case the contract is not traded during the last half-hour, the daily settlement price shall be the theoretical price computed for the contract.
Clearing Member are responsible to collect and settle the daily mark to market profits/loses incurred by the Trading Member and their clients clearing and settling through them. The pay-in and pay-out of the mark-to-market settlement is on T+1.
SETTLEMENT MECHANISM
Final Settlement: On expiry of the Futures market , all positions of a CM , as existing at the close of trading hours on the expiry day, are marked to market at the final settlement price of the contract , and the resulting profit/loss shall be settled in cash.
The loss/profit amount shall be debited /credited to the relevant CM’s on T+1 Day.
Final settlement price shall be the closing price of the underlying security in the capital market segment of the NSE/BSE, on the expiration day of the futures contract.
SETTLEMENT MECHANISM
Premium Settlement: Buyers of option contracts are liable to pay the premium amount to the sellers.
The pay-in and pay-out of the premium settlement is on T+1 days.
Exercise Settlement: Interim Exercise Settlement: An investor can exercise his in-the-money options at any time during trading hours.
It shall be effected at the close of the trading hours ,on the day of exercise.
Valid exercised options contracts shall be assigned to short positions in the option contract with the same series (I.e having same underlying, same expiry date and same strike price), on a random basis.
SETTLEMENT MECHANISM The investor who has exercised the option
will receive the exercised settlement value per unit of the option from the investor who has been assigned the option contract.
Exercise settlement value is the difference between the strike price and the exercise price.
Exercise settlement price is the closing price of the security on which the option was purchased .
The settlement is on T+1 days.
SETTLEMENT MECHANISM Exercise Settlement : Final Exercise
settlement shall be effected for all open long in-the-money strike price options existing at the close of trading hours, on the expiration day of an option contract.
All such long positions shall be exercised and automatically assigned to short positions in option contracts with the same series, on a random basis.
Final Settlement on T+1 days.
The leverage and liquidity offered by major futures contracts - such as the Nikkei 225, the S&P 500 or Eurodollars - means that these obligations, once in place, mount very quickly; thus bringing down an institution with lightning speed. This is in stark contrast to bad loans or cash investments whose ill-effects takes years to ruin an institution as demonstrated by the cases of British & Commonwealth Bank or Bank of Credit and Commerce International (BCCI).
REFERENCES Black-Scholes and Beyond:Option Pricing Models:
By Neil A.Chriss Applied Maths for Derivatives: By John S.Martin . Derivative: By Paul Wilmott An Introduction to Derivative:-By Don M.Chance Advanced Modeling in Finance using Excell and
VBA: By Marry Jackson and Mike Staunton Option Volatility & Pricing ,Advanced Trading
Strategies and Techniques:Sheldon Natenberg
REFERENCES Black-Scholes and Beyond:Option Pricing Models:
By Neil A.Chriss Applied Maths for Derivatives: By John S.Martin . Derivative: By Paul Wilmott An Introduction to Derivative:-By Don M.Chance Advanced Modeling in Finance using Excell and
VBA: By Marry Jackson and Mike Staunton Option Volatility & Pricing ,Advanced Trading
Strategies and Techniques:Sheldon Natenberg
Thank YouThank You
