Adfin Swaps Theory

Adfin Swaps Theory Guide

Adfin Swaps - Theory Guide

Adfin Swaps - Theory Guide Last Revised 05 March 03 Copyright © 2003 Reuters. All rights reserved. Except as permitted by law, no part of this document may be reproduced or transmitted by any process or means without the prior consent of Reuters. Reuters, by publishing this document, does not guarantee that any information contained herein is and will remain accurate or that use of the information will ensure correct and faultless operation of the relevant service or equipment. Reuters, its agents, and employees shall not be held liable to or through any user for any loss or damage whatsoever resulting from reliance on the information contained herein. Reuters and the Reuters sphere logo are registered trademarks and trademarks of the Reuters group of companies around the world. ADFIN, KOBRA, and KONDOR are registered trademarks, and Reuters Analytic Data System (ADS), Reuters CashFlow (RCF), Reuters Data Contribution Servers (DCS), Reuters Data Transformation System (DTS), Reuters Dealing 2000-2, Reuters Dealing 3000, Reuters Enterprise Licensing System (ELS), Reuters Integrated Data Network (IDN), Reuters KreditNet, Reuters KVAR+, Reuters Market Data System (RMDS), Reuters Network Management System (NMS), Reuters News 2000, Reuters Optimizing Contribution Server (OCS), Reuters Risk@ccess, Reuters Trade@ccess, Reuters Trade Processing (RTP), Reuters Triarch are trademarks of the Reuters group of companies around the world. Adobe, Acrobat, FrameMaker, and PostScript are trademarks of Adobe Systems Inc. BEA WebLogic Server is a trademark of BEA Systems. Clearing21 is a registered trademark of CLEARNET S.A. Hewlett-Packard is a registered trademark of Hewlett-Packard Company. IBM is a registered trademark, and IBM AIX, RISC System/6000 (RS6000), and Power PC are trademarks of International Business Machines Corporation. Intel is a registered trademark of Intel Corp. Java, Solaris, Sun, and SunOS are trademarks or registered trademarks of Sun Microsystems Inc. in the U.S.A. and other countries. libwww: Copyright © 1994-2000 World Wide Web Consortium, (Massachusetts Institute of Technology, Institut National de Recherche en Informatique et en Automatique, Keio University). All Rights Reserved. See W3C License http://www.w3.org/Consortium/Legal/ for more details. Copyright © 1995 CERN.Reuters ADS includes computer software created and made available by CERN. This acknowledgment shall be mentioned in full in any product which includes the CERN computer software included herein or parts thereof. Microsoft, MS-DOS, Visual Basic, Windows, Windows NT, Windows XP, and Windows 2000 are registered trademarks, and ActiveX, Microsoft Excel, Microsoft Internet Explorer, and Microsoft Word are products of Microsoft Corp. in the U.S.A. and other countries. MOTIF is a trademark of the Open Software Foundation in the U.S.A. and other countries. Netscape is a registered trademark of Netscape Communications Corporation in the U.S.A. and other countries. NuTCRACKER is a registered trademark of MKS. Olectra and Olectra Chart are trademarks of KL Group Inc. OPEN LOOK is a registered trademark of Novell Inc. Oracle is a trademark of Oracle Corporation. PASSOLO is a registered trademark of PASS Engineering GmbH in Germany.PowerTier is a trademark of Persistence Software Inc. in the U.S.A. and other countries. RiskMetrics is a trademark of J.P. Morgan. SYBASE is a registered trademark, SYBASE SQL is a trademark, SYBASE Adaptive Server, SYBASE Open Client, SYBASE Open Server, SYBASE Replication Server, and SYBASE RSSD, are products of SYBASE Inc. SPARC trademarks are trademarks or registered trademarks of SPARC International Inc. licensed exclusively to Sun Microsystems Inc. UNIX is a registered trademark in the U.S.A. and other countries, licensed exclusively through X/Open Company Limited. TIB and TIBCO are registered trademarks, and TIBCO Information Cache, TIBCO Hawk, and TIBCO Rendezvous are trademarks of TIBCO Software Inc. Visigenic and VisiBroker are trademarks of Visigenic Software Inc. X Window System is a trademark of Massachusetts Institute of Technology. Acknowledgement is made to all other brand or product names referred to in the text that are registered trademarks, trademarks, or trade names of their respective owners. Your comments are welcome Please provide feedback on the Reuters guides and on-line help by sending your comments by e-mail to: [email protected]. Published by Reuters, 85 Fleet Street, London, EC4P 4AJ, UK.

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TABLE OF CONTENTS

1. INTRODUCING ADFIN SWAPS ....................................................................................5

1.1. PRODUCT DESCRIPTION ...........................................................................................................5

1.2. FUNCTIONS OVERVIEW .............................................................................................................5

1.3. DEFAULT SETTINGS ...................................................................................................................5

2. INTEREST RATE HEDGING INSTRUMENTS ..............................................................7

2.1. HEDGING PRINCIPLES ...............................................................................................................7 2.1.1. Interest Rate Hedging ................................................................................................................7 2.1.2. Single Period Hedging vs Multiple Periods Hedging .................................................................7 2.1.3. Interest Rate Guarantee vs Option Based Products .................................................................7

2.2. SINGLE PERIOD HEDGING.........................................................................................................7 2.2.1. FRAs and Interest Rate Futures ................................................................................................7 2.2.2. IRGs and Interest Rate Futures Options ...................................................................................8

2.3. MULTIPLE PERIODS HEDGING..................................................................................................8 2.3.1. Interest Rate Swaps...................................................................................................................8 2.3.2. Caps, Floors and Collars ...........................................................................................................8

3. SWAP MARKET OVERVIEW ......................................................................................10

3.1. MARKET CONVENTIONS ..........................................................................................................10 3.1.1. Interest Rate Convention .........................................................................................................10 3.1.2. Day Count Basis ......................................................................................................................10 3.1.3. Date Moving Convention..........................................................................................................11 3.1.4. End-of-Month Convention ........................................................................................................12

3.2. CHARACTERISTICS OF A SWAP..............................................................................................12 3.2.1. Notional Principal .....................................................................................................................12 3.2.2. Interest Payments ....................................................................................................................13 3.2.3. Effective Date...........................................................................................................................13 3.2.4. Reset Dates .............................................................................................................................13 3.2.5. Calculation Periods ..................................................................................................................13 3.2.6. Payment Dates.........................................................................................................................14 3.2.7. Rounding Capabilities for Swaps.............................................................................................14

3.3. SWAP VALUATION AND PRICING............................................................................................15 3.3.1. Terminology .............................................................................................................................15 3.3.2. Swap Valuation ........................................................................................................................16

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3.3.3. Swap Pricing ............................................................................................................................17

3.4. OVERNIGHT INDEXED SWAP...................................................................................................18 3.4.1. OIS Definition ...........................................................................................................................18 3.4.2. Cash Flow Structure ................................................................................................................18 3.4.3. Valuation and Pricing ...............................................................................................................19

4. IRS STYLE DATABASE ..............................................................................................20

4.1. IRS STYLE ..................................................................................................................................20

4.2. IRS STYLE MANAGEMENT WINDOW ......................................................................................20

4.3. IRS STYLE STRUCTURE WINDOW ..........................................................................................21

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1. INTRODUCING ADFIN SWAPS

1.1. PRODUCT DESCRIPTION Adfin Swaps is a module of PowerPlus Pro 4.5 not only dedicated to the valuation of existing swaps but also to the pricing of new swap structures providing ready-to-use models and user-friendly functions. Adfin Swaps covers most interest rate swaps and currency swaps based on all types of floating rate references, either pre-determined (i.e. the rate that applies is known at the beginning of the period) such as the 3-month LIBOR, or post-determined (i.e. the rate that applies is known at the end of the period) such as the Overnight Indexed Swap. Adfin Swaps also supports non-standard swap types such as broken and backset swaps. All standard day count, end-of-month and date moving conventions are supported by Adfin Swaps. Calendar management and date calculation are handled by a separate software module called Adfin Dates. Adfin Dates includes preset calendars corresponding to the world´s major countries, and no prior knowledge of foreign holidays is required to perform accurate calculation on non-working days. Please refer to the Adfin Dates documentation and on-line help for further information concerning the corresponding topics.

1.2. FUNCTIONS OVERVIEW Adfin Swaps is also a function library designed to handle most swap analytics. It provides the user with an easy-to-use toolbox for creating his/her own templates with the spreadsheet application. Adfin Swaps functions include:

net present value calculation cash flow generation swap solving

1.3. DEFAULT SETTINGS Adfin Swaps uses default settings for some of its calculations. To set any of these default settings, use the default setting dialog box. The available settings are described below. Paid Leg Type The sign applied by Adfin Swaps to the fixed and floating payments depends on the paid leg type. The default type is used unless another type is specified with the keyword PAID in the IrsStructure Argument. Adjustment Mode The adjustment mode is the method used to calculate the coupon dates of the swaps (see Calculation Periods). This method is used unless another mode is specified using the keyword CFADJ in the IrsStructure Argument.

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Date Conventions The date moving convention is the convention that applies when a calculated date falls on a non-working day. This convention is used unless another convention is specified using the keyword DMC in the IrsStructure Argument. The end-of-month convention is the convention that applies when a calculated date falls on the last day of a month. This convention is used unless another convention is specified using the keyword EMC in the IrsStructure Argument.

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2. INTEREST RATE HEDGING INSTRUMENTS

2.1. HEDGING PRINCIPLES

2.1.1. Interest Rate Hedging Hedging is a technique that allows an entity already exposed to risk, to reduce or eliminate this exposure by adopting an opposite position using hedging instruments. The interest rate risk arises from the impact of fluctuating interest rates. The most common exposure is simply the level of interest rates, but some entities may be vulnerable to the shape of the yield curve.

2.1.2. Single Period Hedging vs Multiple Periods Hedging One key factor in hedging is the term during which the entity wants to be protected against the interest rate risk. Single period instruments such as FRAs and interest rate futures can be used to obtain protection against rate movements for a specified future period. For longer terms, hedging can be achieved with strips of single-period instruments covering the term in several successive periods such as interest rate swaps.

2.1.3. Interest Rate Guarantee vs Option Based Products Another key factor in hedging is the type of protection required. A complete protection against interest rate risk means a guaranteed interest rate for months or years into the future. This complete elimination of risk also means the avoidance of beneficial outcomes as well as bad ones. Option-based products such as caps, floors and collars are the alternative solution to provide protection against the downside while preserving the opportunity to benefit from the upside.

2.2. SINGLE PERIOD HEDGING

2.2.1. FRAs and Interest Rate Futures FRAs and futures are contracts made between two parties that call for some specific action, usually the delivery of some underlying asset, to take place at a future date. Futures contracts differ from forward contracts in several ways as described below. FRAs An FRA, or Forward Rate Agreement, is an agreement between two parties concerning a forward-forward loan granted at a fixed interest rate. It provides a protection against a movement in interest rates. The buyer of an FRA is the borrower, and is therefore protected against a rise in interest rates. The seller of an FRA is conversely protected against a fall in interest rates. No actual lending or borrowing takes place under an FRA. The notional principal amount is not exchanged, but it is used to calculate the settlement sum which compensates for the difference between the interest rate originally agreed and that prevailing when the FRA expires. In practice, the rate is generally not determined at the beginning of the contract period (settlement date), but two days earlier on the fixing date. Moreover, the settlement sum is usually paid on the settlement date, that is at the beginning of the underlying loan or deposit. That is why this sum is

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adjusted to compensate the interest that could be earned if it was invested from the settlement date to the maturity date. Interest Rate Futures Unlike FRAs, future contracts trade on futures exchanges and are highly standardized. A short-term interest rate futures contract fixes the interest rate that will apply during a future period which begins on a pre-defined delivery date. Buying a futures contracts is equivalent to making a fixed-rate deposit, whereas selling a futures contract is equivalent to borrowing. Interest rate futures contracts are quoted on an indexed price defined as 100 minus the reference interest rate in percent. This definition ensures that, no matter what occurs during the life of the contract, its final price always matches that in the cash market.

2.2.2. IRGs and Interest Rate Futures Options FRAs and interest rate futures prevent from benefiting from positive interest rate fluctuations. Option-based products such as IRGs and interest rate futures options allow to benefit from better cash market conditions when the option expires. IRGs A borrower wishing to be protected for a single short period in the future against a rise in interest rates can fix his borrowing rate, either by buying FRAs, or by selling futures. He then avoids the risk but he loses the opportunity to take advantage of lower borrowing rates at the beginning of the hedging period. On the other hand, a call on a FRA (Interest Rate Guarantee) provides the interest rate protection by capping the borrowing rate at the strike price, but also allows to benefit from a fall in interest rates simply by letting the option expire. Interest Rate Futures Options Option on an interest rate futures contract if similar to IRGs except that they are traded on futures exchanges and the terms of such contracts are completely standardized.

2.3. MULTIPLE PERIODS HEDGING

2.3.1. Interest Rate Swaps If a borrower requires finance for a long term, it would normally only be available on a floating-rate basis. The term would be split into a number of periods, and the interest rate for each successive period would be fixed at the start of the period. To obtain protection under such circumstances, the borrower could fix the rate by buying a strip of FRAs, or by selling a strip of futures. The interest rate swap, or IRS, is simply a tailor-made instrument equivalent of a strip of FRAs.

2.3.2. Caps, Floors and Collars Caps, floors and collars are interest rate risk management products based on strips of options. Like interest rate swaps, they allow to hedge a long-term exposure that spans multiple periods, each of which succeeds the other. Contrary to Interest Rate Swaps, they still allow benefiting from advantageous market conditions.

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Caps Borrowing at a fixed-rate while being able to benefit from lower interest rates on a long term period is possible using a strip of call options on FRAs (or put options on interest rate futures), or interest rate cap. Each one of the individual options is called a caplet. In practice, the seller of the cap will pay the cap holder (purchaser) the difference between the prevailing market reference rate and the contract ceiling rate each time the market rate is greater than the cap rate. Thus, the borrower buying a cap obtains protection against higher market rates. Floors An interest rate floor is a multi-periodic interest rate option identical to an interest rate cap except that the seller of a floor pays the purchaser when the reference rate drops below the floor rate. If interest rates fall through the floor level on any reset date, the relevant option or floorlet will be exercised. Collars The combination of selling a floor at a lower strike rate and buying a cap at a higher strike rate is called a collar. Collars are widely used for hedging interest rate risk over an extended period because they provide protection against a rise in interest rates as well as benefit from a fall. Collars can be defined as:

FloorCapCollar −= Where Cap : caplet value Floor : floorlet value Vanilla, Barrier, and Digital Caps and Floors Adfin Analytics enables you to price standard Vanilla caps and floors, as well as Barrier and Digital ones. See Also Vanilla caps pricing Barrier caps pricing Digital caps pricing

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3. SWAP MARKET OVERVIEW

3.1. MARKET CONVENTIONS

3.1.1. Interest Rate Convention The calculation of the interest paid by an investment of principal P, at a fixed annual interest rate r, during the time in years t, requires the choice of an interest rate convention. Money Market Basis The money market basis calculation assumes that the interest is proportional to the length of the investment (pro rata temporis):

Interest P r t= . . Actuarial basis The actuarial basis calculation assumes that the interest is compounded (reinvested) during the length of the investment:

Interest P r t= + −(( ) )1 1 Notes

To be fully defined, the coupon calculation method must include an interest rate convention and a day count convention that indicates how the maturity factor t is calculated. See Day Count Basis for detail.

The term compounding may also be used to indicate that some coupons are not actually paid but reinvested. See Payment Dates for detail.

See also Coupon calculation method keyword CCM in:

IrsStructure Argument CsStructure Argument SwapStructure Argument

3.1.2. Day Count Basis The day count basis is used to calculate the payments exchanged in the swap transaction. The basis applicable should be defined for each leg of the swap. The available bases are described below. Actual/Actual For the calculation or compounding period or portion of period that falls on a non-leap year: Nb Days : Actual number of days in the period or portion of period Year Length : 365

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For the calculation or compounding period or portion of period that falls on a leap year: Nb Days : Actual number of days in the period or portion of period Year Length : 366 Actual/365 (Fixed) Nb Days : Actual number of days in the calculation or compounding period (regardless of leap

years) Year Length : 365 Actual/360 Nb Days : Actual number of days in the calculation or compounding period Year Length : 360 30/360 or Actuarial basis Nb Days : Actual number of days in the calculation or compounding period calculated on the

basis of a year of 360 days with twelve 30-day months unless: The last day of the period is the 31st day of a month and the first day of the period is a day other than the 30th or 31st day of a month, in which case the month that includes the last day shall not be considered to be shortened to a 30-day month

•

• The last day of the period is the last day of the month of February, in which case the month of February shall not be considered to be lengthened to a 30-day month

Year Length : 360 30E/360 or Eurobond Basis Nb Days : Actual number of days in the calculation or compounding period calculated on the

basis of a year of 360 days with twelve 30-day months (regardless of the date of the first day or last day of the period)

Year Length : 360 Notes

To be fully defined, the coupon calculation method must include a day count convention and an interest rate convention that indicates on which basis the interest is calculated. See Interest Rate Convention for detail.

The day count basis of an interest rate swap is generally consistent with the basis on which the floating rate reference is quoted.

See also Coupon calculation method keyword CCM in:


3.1.3. Date Moving Convention The date moving convention is used to adjust the period dates and the payment dates when they fall on a non-business day.

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The available conventions are described below. None The date is not moved. Preceding The date is moved to the preceding business day. Following The date is moved to the following business day. Modified Following The date is moved to the following business day, unless it causes the date to be pushed into the next month (in this latter case, the last working day of the month is used). See also Date moving convention keyword DMC in:


3.1.4. End-of-Month Convention The end-of-month convention is used when a period is added to either the thirtieth day of a month other than February, or the last day of the month of February. The resulting date depends on the convention used as shown below. Same The date numerically corresponds to the calculation date (unless there is no such day, in which case the date is set to the last day of the month). Last The date is set to the last day of the month in all cases. See also End-of-month convention keyword EMC in:


3.2. CHARACTERISTICS OF A SWAP

3.2.1. Notional Principal In a swap contract, both parties agree to exchange at certain times in the future some cash flows (called interest payments or coupons) calculated on different bases. One element needed for the calculation of those cash flows is the nominal principal amount in the agreed currency.

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The notional principal may or may not be actually exchanged. For interest rate swaps, the principal is never exchanged. For currency swaps, the principals in both currencies are exchanged sometimes at the swap start date, and always at the swap end date. Instead of remaining constant, the notional principal can vary through the life of the swap according to a pre-determined pattern. In an amortizing swap, the principal reduces in successive periods. In an accreting or step-up swap, the principal increases gradually over time. If the principal reduces in some periods and increases in others, the swap is described as a roller-coaster swap.

3.2.2. Interest Payments Two of the key items which must be agreed for a swap contract are the payment basis and the payment frequency. Interest payments are usually annual, semi-annual, or quarterly, but their frequency may differ for both the paid and the received legs. In a standard interest rate swap, one party makes to the other party periodic payments based on a fixed rate (this series of cash flows is referred to as the fixed leg), while the other party pays to the first party, on the same or another periodic basis, some floating amounts determined during the lifetime of the swap by reference to a specific market rate, called the floating rate reference or floating rate option (this series of cash flows is referred to as the floating leg). In a currency swap, the legs may be either both fixed, or both floating, or one fixed and the other floating. Besides, the currencies of the two legs are different, and the notional principal is always exchanged on the swap maturity date.

3.2.3. Effective Date The effective date is the date when interests start to accrue on both legs. This date is usually one or two business days after the trade date.

3.2.4. Reset Dates The reset date is the date when the floating rate for the next period is determined. It generally occurs one or two business days before the beginning of the period on which the floating rate applies. The first reset date for a pre-determined floating rate reference occurs always before the swap effective date and is usually equal to the trade date.

3.2.5. Calculation Periods The calculation period is the period during which the paid and received rates defined for the period apply. Coupons start to accrue at the calculation period start date, and end to accrue at the calculation period end date. This period is also called the compounding period. The start date of the first period is always equal to the effective date. Subsequent period start dates are also always equal to the preceding period end dates. The calculation periods are then fully determined as soon as all period end dates are known. Adfin Analytics enables you to handle the calculation periods by specifying a combination of the cash flow adjustment keyword CFADJ and the reference date keyword REFDATE in the SwapStructure or IrsStructure arguments. The three algorithms available in Adfin Swaps for the end dates calculation are described below.

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Unadjusted Mode Use the combination CFADJ:NO REFDATE:MATURITY to apply the Unadjusted Mode. The i-th period end date occurs the day that numerically corresponds to the swap end date in the month that is i periods after the month of the effective date. The end-of-month convention applies if there is no such day. Standard Mode Use the combination CFADJ:YES REFDATE:MATURITY to apply the Standard Mode. The i-th period end date occurs the day that numerically corresponds to the swap end date in the month that is i periods after the month of the effective date (the end-of-month convention applies if there is no such day), unless this date is a non-business day (in which case the date is adjusted using the date moving convention). FRN Mode Use the combination CFADJ:YES REFDATE:ISSUE to apply the FRN Mode. The first period end date occurs the day that numerically corresponds to the swap start date in the month that is one period after the month of the effective date, unless this date is a non-business day. The (i+1)-th period end date occurs the day that numerically corresponds to the i-th period end date in the month that is one period after the month of the i-th period end date, unless this date is a non-business day. Adjustments are made using the end-of-month convention and the date moving convention like in the Standard Mode. Note Since the payment frequencies for the paid and the received legs can be different, the number of calculations periods in the swap lifetime can be different for both legs. See also Reference date keyword REFDATE and cash flow adjustment method keyword CFADJ in IrsStructure Argument and SwapStructure Argument

3.2.6. Payment Dates One interest payment ends accruing at the end of the calculation period of the corresponding leg. However, there may be a delay between the calculation period end date and the actual payment date. When existing, this delay is generally defined as a number of business days. The payment frequency for the floating leg may also be different from the coupon frequency. In other words, the floating rate interest is compounded on several calculation periods until payment occurs (in such cases, the floating leg payments generally occur on the fixed leg payment dates). See also Payment delay keyword PDELAY in IrsStructure Argument

3.2.7. Rounding Capabilities for Swaps Adfin Swaps supports the new keyword CRND to define the rounding mode for the output coupon value. The available rounding modes with their respective formulas are the following:

CRND:0.001:UP:

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CRND:0.001:DOWN:

CRND:0.001:NEAR:

Where x : the value to round floor : the whole part The precision i is specified by CRND:i:{UP, DOWN, NEAR}. In the previous formulas, i is equal to 0.001. See also Coupon calculation rounding keyword CRND in:

IrsStructure Argument SwapStructure Argument

3.3. SWAP VALUATION AND PRICING

3.3.1. Terminology Several different terms are used in the field of swaps financial engineering to describe different techniques. This section aims at clarifying those terms. Valuation Valuing a swap consists in finding the net present value of an existing swap for which the rates have been already set. Netting Netting is very similar to valuation. The only difference lies in the fact that netting generally describes how the swap should be valued in case of a counterparty failure. The terms netting and valuation will therefore be considered as synonymous in the remainder of this documentation. Pricing Swap pricing usually implies the calculation of a swap rate such as the net present value equals a predefined value (generally zero). See also Swap Valuation Swap Pricing

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3.3.2. Swap Valuation Any swap, no matter how complex, can be described as two series of cash flows, one for the paid leg (cash outflows), and another for the received leg (cash inflows). The net present value of any of those legs is the sum of the present value of the corresponding cash flows. The calculation of the net present value of a swap leg is a two-step process. First, the payment amounts (or cash flows) have to be estimated. Second, those payments have to be valued by applying zero-coupon rates. Both steps involve the use of a zero-coupon curve. Cash Flows Amount The interest payments are calculated using the standard formulas:

CF P d rBi =. . for a money market basis

CF P ri

dB= + −(( ) )1 1 for an actuarial basis

Where CFi : future cash flow occurring at time i P : notional principal d : number of days in the calculation period r : fixed or floating annualized interest rate applicable for the period B : day count basis For the fixed leg of an interest rate swap, the coupon rate r applicable for the period is known right from the trade date, so all fixed payments are known in advance. On the contrary, floating rate payments have to be estimated calculating the forward floating rates from the zero-coupon yield curve. The only exception to this is the next cash flow (i.e. paid or received at the end of the current calculation period) that can be precisely calculated for pre-determined floating rate options (the coupon rate r applicable for the period is indeed known a few days before the period start date). In Adfin Swaps, the CCM keyword allows the user to specify the coupon calculation method (see the IrsStructure, CsStructure, and SwapStructure Arguments for detail). Cash Flows Present Value A set of discount factors di can be determined from the zero-coupon yield curve. For periods longer than one year, zero-coupon rates are calculated assuming compounded interest, and discount factors can be obtained using the formula:

drii

=+

11( ) ti

Where di : discount factor at time i ri : zero-coupon rate from value date to time i ti : time in years from value date to time i

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If a cash flow occurs at a time in the future for which the zero-coupon rate is not known, the zero-coupon rate or the corresponding discount factor must be interpolated (Adfin Swaps offers appropriate methods for both coupon rate and discount factor interpolations). The present value of a cash flow is then:

PF d CFi i i= . Where PFi : present value of the future cash flow occurring at time i CFi : future cash flow occurring at time i di : discount factor at time i Net Present Value of Interest Rate Swaps The net present value of an interest rate swap is the difference between the net present values of the received and the paid legs:

NPV d CF d CFi ii

N

j jj

M

= −= =∑ ∑. .

1 1

Where CFi : cash flow received at time i CFj : cash flow paid at time j N : number of cash flows in the received leg M : number of cash flows in the paid leg Net Present Value of Currency Swaps In a currency swap, one of both currencies is chosen to be the discount currency. The net present value of the leg of the discount currency is calculated as described above for an interest rate swap. The net present value of the other leg is calculated converting each cash flow to the discount currency using the corresponding outright rate (calculated from the spot rate and the swap point at the cash flow date) and discounting them using the zero-coupon curve of the discount currency. Notes

For accounting purposes, it may be useful to calculate the accrued interest, i.e. the portion of the current coupon already due or owned since the calculation period start date (the accrued interest is calculated pro rata temporis from the coupon value).

CURVESHIFT enables you to apply a shift of i to the rates of your yield curve. Adfin Swaps then gives you the ability to take into account the risk of a swap in your calculations using Adfin Swaps functions. You can apply the parallel shift, whatever the rate model you use (Yield to Maturity, Hull and White, Vasicek-Fong, Black and Scholes, etc.).

For more information about the calculation of implied forward rates and discount factors, see the Adfin Term Structure online help.

3.3.3. Swap Pricing Two counter parties contracting a swap will generally choose either the fixed rate, or the margin above or below the floating reference rate option, such that the net present value of the swap is zero.

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Fixed Rate Pricing To price the fixed rate for any kind of interest rate swap, the floating leg is first valued using a set of zero-coupon rates (or discount factors), and the fixed rate you search is the one which makes the present value of the fixed leg equal to the present value of the floating leg:

rP d t r

P d t

i i i ii

N

j j jj

M= =

=

∑

∑

. . .

. .

1

1

Where r : annualized interest rate of the fixed leg ri : implied forward rate of the floating leg calculation period i dj : discount factor at the fixed leg calculation period end date j di : discount factor at the floating leg calculation period end date i tj : time in years of the fixed leg calculation period j ti : time in years of the floating leg calculation period i Pj : notional principal of the fixed leg calculation period j Pi : notional principal of the floating leg calculation period i M : number of cash flows in the fixed leg N : number of cash flows in the floating leg In standard swap contracts, the notional principal is constant through the swap life. The above formula becomes simpler, and the fixed rate can be determined without the knowledge of its value.

3.4. OVERNIGHT INDEXED SWAP

3.4.1. OIS Definition An Overnight Indexed Swap, also called call money swap, is a fixed/floating interest rate swap with the floating leg tied to a daily overnight (or Tom/Next in some markets) rate reference. The term generally ranges from one week to one year.

3.4.2. Cash Flow Structure The two parties to an OIS agree to exchange at maturity, on the agreed notional amount, the difference between interest accrued at the agreed fixed rate and interest accrued through compounding the floating index rate. There is no exchange of principal.

Net paymentFloating

coupon

Fixed coupon

Start date

Trade date

The start date is generally two trading days or more (forward transactions) following trade date, but it can also be the same as the trade date. The maturity date is on the same day as the start date of the maturity month (or next open business day). The payment is always netted on the maturity date, even if it can be actually deferred a couple of days later.

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Coupon Calculations Consider an OIS with a fixed rate R, a notional amount N and d days from effective date (i.e. start date) to maturity date. The fixed coupon is calculated as follows:

basisdRNPfix ××=

The compounded settlement rate is given by:

dbasis

basisnrCSR

p

i

ii ×

−

×

+= ∏=1

11

Where

i : index for open business days p : number of open business days ri : overnight or Tom/Next index rate for day i (rp is the rate one or two business before

maturity) ni : number of days from which ri is valid (normally one day or three days for

weekends) Therefore we have:

∑=

=p

ii dn

1

This compounded settlement rate is then rounded, and the floating coupon is calculated as the fixed coupon:

basisdCSRNPfloat ××=

3.4.3. Valuation and Pricing Common swap techniques for pricing and valuing are used for OIS. Briefly, since OIS replicate cash, building a zero-coupon yield curve from them is the same as building from cash rate. For each benchmark, with Z the zero-coupon rate and R the OIS swap rate, we have:

( )

×+=+

basisdRZ

d11 365

Valuing is done projecting unknown rates using a zero-coupon yield curve built from benchmark swap rates, and then discounting the cash flows using the same zero curve. Pricing is done calculating the present value and solving for the fixed rate that gives a present value of zero.

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4. IRS STYLE DATABASE

4.1. IRS STYLE In order to avoid fastidious definitions of numerous attributes in the extended parameter IrsStructure, Adfin Swaps includes an IRS style database. This IRS style database contains about 20 different swap structures which correspond to the major countries, and is therefore ready-to-use. Those default IRS styles may be edited but cannot be modified by the user. However, new IRS styles can be added to the database if needed. Each IRS style stored in the database is referred to by a code (such as USD_AM32L,...). This code can be used as a new keyword (with no corresponding value) for any IrsStructure Argument. For instance, using DEM_AB6L as IrsStructure argument stands for "LBOTH CLDR:GER ACC:AA ARND:NO CFADJ:YES CRND:NO DMC:MODIFIED EMC:SAMEDAY IC:S1 PDELAY:0 REFDATE:MATURITY RP:1 RT:BULLET XD:NO LPAID LTYPE:FIXED CCM:BB00 FRQ:Y LRECEIVED LTYPE:FLOAT SPREAD:0 CCM:MMA0 FRQ:S". This new keyword can be followed by others attributes which will overwrite part of the data defined for the IRS style (e.g. the default coupon frequency for the fixed leg will be set to semi-annual using the string "DEM_AB6L LFIXED FRQ:2"). Note Holidays are managed through calendars defined in the Adfin Dates calendar style database.

4.2. IRS STYLE MANAGEMENT WINDOW The IRS styles defined in the database are displayed in the IRS style list. From that window, the user can manage the IRS style database as detailed below. Editing an Existing IRS Style An IRS style should be edited to view or modify its features.

To edit an IRS style

Select an IRS style in the IRS style list, and choose Open. Or double click the IRS style.

See IRS Style Structure Window for information about working with the edited IRS style. Deleting an Existing IRS Style

To delete an IRS style

Select an IRS style in the IRS style list, and choose Delete. Creating a New IRS Style When creating a new IRS style, the user has the option to create it from scratch or make a copy of an existing IRS style.

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To create an IRS style

Select an IRS style in the IRS style list, and choose New to create a new IRS style as the copy of an existing one.

Or choose New without selecting any IRS style to create an IRS style from defaults. See IRS Style Structure Window for information about working with the newly-created IRS style. Exiting the IRS Style Management Window

To exit the IRS style management window

Choose Close.

4.3. IRS STYLE STRUCTURE WINDOW The IRS style structure window is used to view or modify the features of an IRS style. The available options are detailed below. Defining the IRS Style

To define the IRS style

1. Enter the IRS style Code. 2. Enter the IRS style Name. 3. Select the proper option for Paid Leg Type. 4. Enter the code of the Calendar that describes the swap holidays. 5. Select the proper option for the fixed and floating legs Coupon Frequency. 6. Select the proper option for the fixed and floating legs Coupon Calculation Method. 7. Select the proper option for the fixed and floating legs Date Moving Convention. 8. Select the proper option for the fixed and floating legs End-of-Month Convention. 9. Select the proper option for the fixed and floating legs cash flows Adjustment Mode (see

Calculation Periods). 10. Select the proper option for the fixed and floating legs Payment Delay (see Payment Dates). 11. Select the proper option for the fixed and floating legs Reference Dates (see Calculation

Periods). 12. Select the proper option for the floating leg Index Reference.

Testing the IRS Style

To test the IRS style

Choose Structure to display the equivalent IRS structure string. Exiting the IRS Style Structure Window

To exit the IRS style structure window

Choose OK to exit and save changes, or Cancel to exit without saving.

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Adfin Swaps Theory