Swaps and Other Derivatives E-Book

Richard R. Flavell

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Finance Series
• Sprache: Englisch

Seitenzahl: 659

Veröffentlichungsjahr: 2012

Beschreibung

“Richard Flavell has a strong theoretical perspective on swaps with considerable practical experience in the actual trading of these instruments. This rare combination makes this welcome updated second edition a useful reference work for market practitioners.”
—Satyajit Das, author of Swaps and Financial Derivatives Library and Traders and Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives

Fully revised and updated from the first edition, Swaps and Other Derivatives, Second Edition, provides a practical explanation of the pricing and evaluation of swaps and interest rate derivatives.

Based on the author’s extensive experience in derivatives and risk management, working as a financial engineer, consultant and trainer for a wide range of institutions across the world this book discusses in detail how many of the wide range of swaps and other derivatives, such as yield curve, index amortisers, inflation-linked, cross-market, volatility, diff and quanto diffs, are priced and hedged. It also describes the modelling of interest rate curves, and the derivation of implied discount factors from both interest rate swap curves, and cross-currency adjusted curves.

There are detailed sections on the risk management of swap and option portfolios using both traditional approaches and also Value-at-Risk. Techniques are provided for the construction of dynamic and robust hedges, using ideas drawn from mathematical programming.

This second edition has expanded sections on the credit derivatives market – its mechanics, how credit default swaps may be priced and hedged, and how default probabilities may be derived from a market strip. It also prices complex swaps with embedded options, such as range accruals, Bermudan swaptions and target accrual redemption notes, by constructing detailed numerical models such as interest rate trees and LIBOR-based simulation. There is also increased discussion around the modelling of volatility smiles and surfaces.

The book is accompanied by a CD-ROM where all the models are replicated, enabling readers to implement the models in practice with the minimum of effort.

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Preface

Extract from the Preface to the First Edition

Preface to the Second Edition

Biography

Worksheets

Abbreviations

Dedication

Chapter 1: Swaps and Other Derivatives

1.1 Introduction

1.2 Applications of Swaps

1.3 An Overview of the Swap Market

1.4 The Evolution of the Swap Market

1.5 Conclusion

Chapter 2: Short-Term Interest Rate Swaps

Objective

2.1 Discounting, the Time Value of Money and Other Matters

2.2 Forward Rate Agreements (FRAs) and Interest Rate Futures

2.3 Short-Term Swaps

2.4 Convexity Bias in Futures

2.5 Forward Valuing a Swap

Chapter 3: Generic Interest Rate Swaps

Objective

3.1 Generic Interest Rate Swaps

3.2 Pricing Through Comparative Advantage

3.3 The Relative Pricing of Generic IRSs

3.4 The Relationship Between the Bond and Swap Markets

3.5 Implying a Discount Function

3.6 Building a Blended Curve

Chapter 4: The Pricing and Valuation of Non-Generic Swaps

Objective

4.1 The Pricing of Simple Non-Generic Swaps: Forward Starts

4.2 Rollercoasters

4.3 Pricing of Simple Non-Generic Swaps: A More Complex Example

4.4 Forward Valuing as an Alternative to Discounting—Revisited

4.5 Swap Valuation

Chapter 5: Asset Packaging

Objective

5.1 Creation and Pricing of a Par Asset Swap

5.2 Creation and Pricing of a Par Maturity Asset Swap

5.3 Discounting, Embedded Loans and Forward Valuing

5.4 Further Extensions to Asset Packaging

Chapter 6: Credit Derivatives

Background and Objective

6.1 Total Return Swaps

6.2 Credit Default Swaps

6.3 Pricing and Hedging of Generic CDSs

6.4 Modelling a CDS

6.5 Pricing and Valuing Non-Generic CDSs

6.6 Basket and Portfolio CDSs

6.7 Credit Exposure Under Swaps

6.8 Appendix: An Outline of the Credit Modelling of Portfolios

Chapter 7: More Complex Swaps

Objective

7.1 Simple Mismatch Swaps

7.2 Average Rate Swaps

7.3 Compound Swaps

7.4 Yield Curve Swaps

7.5 Convexity Effects of Swaps

7.6 Appendix: Measuring the Convexity Effect

Chapter 8: Cross-Market and Other Market Swaps

Objective

8.1 Overnight Indexed Swaps

8.2 Cross-Market Basis Swaps

8.3 Equity and Commodity Swaps

8.4 Longevity Swaps

8.5 Inflation Swaps

8.6 Volatility Swaps

Chapter 9: Cross-Currency Swaps

Objective

9.1 Floating-Floating Cross-Currency Swaps

9.2 Pricing and Hedging of CCBSs

9.3 Ccbss and Discounting

9.4 Fixed-Floating Cross-Currency Swaps

9.5 Floating-Floating Swaps Continued

9.6 Fixed-Fixed Cross-Currency Swaps

9.7 Cross-Currency Swap Valuation

9.8 Dual-Currency Swaps

9.9 Cross-Currency Equity Swaps

9.10 Conclusion

9.11 Appendix: Quanto Adjustments

Chapter 10: OTC Options

Objective

10.1 Introduction

10.2 The Black Option-Pricing Model

10.3 Interest Rate Volatility

10.4 Par and Forward Volatilities

10.5 Caps, Floors and Collars

10.6 Digital Options

10.7 Embedded Structures

10.8 Swaptions

10.9 Structures with Embedded Swaptions

10.10 Options on Credit Default Swaps

10.11 FX Options

10.12 Hedging FX Options

10.13 Appendix: The SABR Model for Stochastic Volatility

Chapter 11: Swapping Structured Products

Objective

11.1 Introduction

11.2 Examples of Some Structured Securities

11.3 Numerical Interest Rate Models

11.4 Simulation Models

11.5 Appendix: Extensions to Numerical Trees

Chapter 12: Traditional Market Risk Management

Objective

12.1 Introduction

12.2 Interest Rate Risk Management

12.3 Gridpoint Risk Management—Market Rates

12.4 Equivalent Portfolios

12.5 Gridpoint Risk Management—Forward Rates

12.6 Gridpoint Risk Management—Zero-Coupon Rates

12.7 Yield Curve Risk Management

12.8 Bond and Swap Futures

12.9 Theta Risk

12.10 Risk Management of IR Option Portfolios

12.11 Hedging of Inflation Swaps

12.12 Appendix: Analysis of Swap Curves

Chapter 13: Value-at-Risk

Objective

13.1 Introduction

13.2 A Very Simple Example

13.3 A Very Simple Example Extended

13.4 Multi-Factor Delta VaR

13.5 Choice of Risk Factors and Cashflow Mapping

13.6 Estimation of Volatility and Correlations

13.7 A Running Example

13.8 Simulation Methods

13.9 Shortcomings and Extensions to Simulation Methods

13.10 Delta-Gamma and Other Methods

13.11 Spread VaR

13.12 Equity VaR

13.13 Shock Testing of VaR

13.14 Stress Testing of VaR

13.15 Appendix: Extreme Value Theory

Index

Swaps and Other Derivatives

For other titles in the Wiley Finance series please see www.wiley.com/finance

This edition first published in 2010Copyright © 2010 John Wiley & Sons Ltd

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ISBN 978-0-470-72191-9

A catalogue record for this book is available from the British Library.

Project Management by OPS Ltd, Gt Yarmouth, Norfolk

Preface

EXTRACT FROM THE PREFACE TO THE FIRST EDITION

This book is designed for financial professionals to understand how the vast bulk of OTC derivatives are used, structured, priced and hedged, and ultimately how to use such derivatives themselves. A wide range of books already exist that describe in conceptual terms how and why such derivatives are used, and it is not the ambition of this book to supplant them. There are also a number of books which describe the pricing and hedging of derivatives, especially exotic ones, primarily in mathematical terms. Whilst exotics are an important and growing segment of the market, by far the majority of derivatives are still very much first generation, and as such relatively straightforward.

For example, interest rate swaps constitute over half of the $100 trillion OTC derivative market, and yet there have been few books published in the last decade that describe how they are created and valued in practical detail. So how do many of the professionals gain their knowledge? One popular way is "learning on the job", reinforced by the odd training course. But swap structures can be quite complex, requiring more than just superficial knowledge, and probably every professional uses a computer-based system, certainly for the booking and regular valuation of trades, and most likely for their initial pricing and risk management. These systems are complex, having to deal with real-world situations, and their practical inner details bear little resemblance to the idealised world of most books. So often, practitioners tend to treat the systems as black boxes, relying on some initial and frequently inadequate range of tests, and hoping their intuition will guide them. The greatest sources of comfort are often the existing customer list of the system (they can’t all be wrong!) and, if the system is replacing an old one, comparative valuations.

The objective of this book is to describe how the pricing, valuation and risk management of generic OTC derivatives may be performed, in sufficient detail and with various alternatives, so that the approaches may be applied in practice. It is based upon some 15 years of varying experience as a financial engineer for ANZ Merchant Bank in London, as a trainer and consultant to banks worldwide, and as Director of Financial Engineering at Lombard Risk Systems responsible for all the mathematics in the various pricing and risk management systems.

The audience for the book is, first, traders, sales people and front-line risk managers. But increasingly such knowledge needs to be more widely spread within financial institutions, such as internal audit, risk control, and IT. Then there are the counterparties such as organisations using derivatives for risk management, who have frequently identified the need for transparent pricing. This need has been exacerbated in recent years as many developed countries now require that these organisations demonstrate the effectiveness of risk management, and also perform regular (usually annual) mark-to-market. Similarly, organisations using complex funding structures want to understand how the structures are created and priced. Turning to the other side, many fund managers and in particular hedge funds are also using derivatives to manage their risk profile, and then to report using one of the Value-at-Risk techniques. This has been particularly true since the collapse of Long Term Capital Management, despite the fact that most implementations of VaR would not have recognised the risk. Other potential readers are the auditors, consultants, and regulators of the banks and their client organisations.

PREFACE TO THE SECOND EDITION

Many of the above statements are still true. The swap market has continued to grow six-fold over the intervening years, to a staggering $328 trillion. Yet, there has been little published to provide guidance and assistance to the professionals in the market. Why was it thought useful to write a second edition? There were two main reasons. First, many readers had suggested changes and developments, which I thought appropriate to include. Second, the exponential growth in credit default swaps and structured securities identified areas which were little discussed in the first edition. This edition attempts to redress that omission.

Institutions offer derivatives with a wide range of maturities, ranging from a few hours (used to provide risk management over the announcement of an economic figure) to perpetuals (i.e. no upfront maturity defined). There is however a golden rule when pricing derivatives, namely always price them off the market that will be used to hedge them. This leads to the first separation in the interest rate swap market between:

Chapter 2:The short end of the curve, which uses cash, futures and occasionally FRAs to hedge swaps. This chapter first discusses the derivation of discount factors from cashrates, and concentrates on the range of alternative approaches that may be used. It then looks at the derivation of forward interest rates, and how FRAs may be priced using cash and futures. The convexity effect is highlighted for future discussion. Finally an approach is introduced that does not require discounting, but permits the introduction of a funding cost.Chapter 3:The medium to long end of the curve. The highly liquid interbank market typically trades plain swaps (usually known as "generic" or "vanilla"), very often between market makers and intermediaries. These are hedged in other financial markets, typically futures for the shorter exposures and bonds for the longer ones. This chapter concentrates initially on the relationship between the bond and swap markets, and how generic swap prices may be implied. It concludes by developing various techniques for the estimation of discount factors from a generic swap curve.Chapter 4:The end-user market provides customers with tailored (i.e. non-generic) swaps designed to meet their specific requirements. Such swaps are not traded as such, but created as one-off structures. This chapter describes a range of simple non-generic swaps, and discusses various techniques for pricing them, including one that requires no discounting. Finally two approaches to the ongoing valuation of an existing (seasoned) swap are demonstrated.Chapter 5:Swaps are often used to restructure new or existing securities. This chapter describes some initial structures, par asset packaging and par maturity asset packaging, that are commonly used.Chapter 6:Credit derivatives effectively evolved from the asset packaging or securitisation markets. The chapter first discusses total return swaps as being the earliest form of credit derivative, but then moves rapidly on to its successor, single-name credit default swaps. The chapter is in three parts. First, a broad description of the mechanics of the market, especially following the Big and Small Bangs in 2009. Second, an analysis of the relationship between asset packaging and the hedging of CDSs, leading to a discussion around the credit basis. Third, a derivation of implied forward default probabilities from CDS prices using a couple of slightly different approaches. This in turn allows the pricing of non-generic CDSs such as forward starts, amortising and floating rate.Chapter 7:This discusses a range of more complex swaps known generally as mismatch swaps. This includes structures such as yield curve (also known as CMSs), in arrears, average rate, and compound. The chapter and its appendix re-introduce the concept of convexity-adjusted pricing more formally.Chapter 8:This introduces a range of what are often called cross-market swaps. These involve the normal interbank floating rate (or indeed a fixed rate) on one side, and another reference rate drawn from another market on the other side, such as an overnight rate, or a base rate, or a mortgage rate, or an inflation rate, or an equity return, and so on. The main purpose of these swaps is to permit people with exposures in the other market to gain access to the range of risk management instruments that exists in the interbank market.Chapter 9:The earliest swap structures were cross-currency swaps, although this market has been long overtaken by interest rate swaps. Nevertheless they possess some unique characteristics and structures. This chapter starts with the fundamental CCS building block, the cross-currency basis swap, and explores its characteristics, uses, pricing and hedging. This employs a novel approach: worst case simulation. The role of CCBSs in the derivation of cross-currency discount factors is also explored. The main other types of swaps are then discussed: fixed-floating, floating-floating, diff, and quanto-diff. Fixed-fixed swaps occupy a special place because they are a general case of long-term FX forward contracts, so the pricing and hedging of these is considered in some detail. Finally swap valuation is revisited because, in the CCS market, such swaps are frequently valued annually and the principals reset to the current exchange rate.Chapter 10:There is an active market in many currencies in medium to long-term options on forward interest rates, usually known as the cap and floor market. Such structures are intimately linked to swaps for two reasons: first, because combinations of options can create swaps and, second, swaps are generally used to hedge them. In many banks, they are actually traded and risk-managed together. This chapter reviews a range of different option structures and touches albeit briefly on option pricing. Volatility plays a crucial role and various techniques for estimation, including transformation from par to forward as well as volatility smiles and volatility spaces, are described in detail. These options are also frequently embedded in many swap structures, and the breakdown and pricing of a range of structures is discussed. There is also an active market in options on forward swaps (aka swaptions or swop-tions) which, not unnaturally, is closely related to the swap market. The pricing and embedding of swaptions is described. The chapter concludes with two sections on FX options. These options are mainly traded OTC, although there is some activity on a few exchanges such as Philadelphia. The first section concentrates on the pricing of these options, and how it may be varied depending on the method of quoting the underlying currencies. The second section shows how traders would dynamically create a delta-neutral hedge for such an option, together with the hedging errors through time.Chapter 11:This chapter concentrates on more complex swaps arising from the need to swap structured securities. It starts by discussing the swapping of range accruals. It goes on to price structures such as callable bonds, Bermudan swaptions and path-dependent products such as target accrual redemption notes and snowballs using both numerical trees and Libor-based simulation.Chapter 12:In the early days of the swap market, swap portfolios were risk-managed either using asset-liability methods such as gapping or the more advanced institutions used bond techniques such as duration. By the late 1980s a number of well-publicised losses had forced banks to develop more appropriate techniques such as gridpoint hedging. These (in today’s eyes) traditional approaches stood the banks in good stead for the next decade. This chapter describes the main techniques of both gridpoint and curve hedging, taking into account both first and second-order sensitivities. In passing, mapping cashflows to gridpoints is also discussed. The use of swap futures, as a relatively new hedging instrument, is also considered. The chapter then extends risk management to interest rate options. Most texts discuss the "Greeks" using short-dated options; unfortunately the discussion often does not apply to long-term options, and so their different characteristics, especially as a function of time, are examined. The effectiveness of some optimisation techniques to construct robust hedges are examined as an alternative to the more traditional delta-gamma methods. Finally, the chapter shows how the same techniques can be used to create an inflation hedge for a portfolio of inflation swaps.Chapter 13:Risk management however is not a static subject, but has evolved rapidly during the latter half of the 1990s and beyond. Traditional risk management operates quite successfully, but there is a very sensible desire by senior management to be able to assess the riskiness of the entire trading operation and even wider. The traditional risk measures are not combinable in any fashion and cannot be used. Value-at-Risk was developed as a family of approaches designed very much to address this objective. It is now being developed further to encompass not only market risk but also credit and even operational risks into the same set of measures.1 This chapter describes the major approaches used to estimate VaR: delta, historic and Monte Carlo simulations, as well as second-order delta-gamma approaches. The advantages and disadvantages of each approach are discussed, along with various extensions such as extreme value theory and sampling strategies. The measurement of spread VaR and equity VaR using either individual stocks or a stock index are also considered. Finally, stress testing or how to make significant moves in the properties of the underlying risk factors (especially correlation) is described.

The book is supported by a full range of detailed spreadsheet models, which underpin all the tables, graphs and figures in the main text. Some of the models have not been described in detail in the text, but hopefully the instructions on the sheets should be adequate. Many of the models are designed so that the reader may implement them in practice without much difficulty.

Many of the ideas, techniques and models described here have been developed over the years with colleagues at both ANZ and Lombard Risk Systems, and through various consulting assignments with a wide range of banks across the world.

BIOGRAPHY

Richard Flavell has spent over twenty years working as a financial engineer, consultant and trainer, specialising in complex derivatives and risk management. He spent seven years as Director of Financial Engineering at Lombard Risk, where he was responsible for the mathematical development and implementation of models in its varied pricing and risk systems. He is currently Chairman of Lucidate, a company which specialises in the provision of consultancy and training to financial institutions.

1 See the proposed Basel Accord (for details see the BIS website: www.bis.org) for the regulatory requirements using VaR-style approaches.

Abbreviations

ABCDSAsset-Backed CDSALMAsset Liability ManagementARCHAutoRegressive Conditional HeteroskedasticASWAsset SWapATMAt The MoneyB&SBlack and ScholesBDTBlack-Derman-ToyBGMBrace-Gatarek-MusielaBISBank for International Settlementc-ccontinuously compoundedCADFCredit-Adjusted Discount FactorCBOTChicago Board of TradeCCBSCross-Currency Basis SwapCCECurrent Credit ExposureCCSCross-Currency SwapCCVNCross-Currency Variable NotionalCDOCollateralised Debt ObligationCEACredit Event AuctionCETCentral European TimeCMEChicago Mercantile ExchangeCMSConstant Maturity SwapCPCommercial PaperCSACredit Support AnnexCTFFCash To First FuturesDCDetermination CommitteeDFDiscount FactorDMODebt Management OfficeDPDirty (purchase) PriceDTCCDepository Trust and Clearing CorporationEBRDEuropean Bank for Reconstruction and DevelopmentECBEuropean Central BankEIBEuropean Investment BankEMEAEurope, Middle East and AfricaEONIAEuro OverNight Index AverageEPEExpected Positive ExposureEVTExtreme Value TheoryFDPForward Default ProbabilityFRFull (or complete) RestructuringFRAForward Rate AgreementFRNFloating Rate NoteFSAFinancial Services AuthorityFXForeign ExchangeG—KGarman—KohlhagenGARCHGeneralised ARCHGCGeneral CollateralGEVGeneralised Extreme ValueGPGeneralised Pareto (Chapter 13);Goal Programming (Chapter 12)HICPHarmonised Index of Consumer PricesHICPXTHICP excluding TobaccoHJMHeath—Jarrow—MortonIBORInter Bank Offer RateIFImplied ForwardIMMInternational Monetary Market (based in CME)IRBInternal Rating BasedIRSInterest Rate SwapISDAInternational Swap and Derivatives AssociationITMInto The MoneyKfWKreditanstalt für Wiederaufbau (Reconstitution Credit Institute)LFLikelihood FunctionLiborLondon inter-bank overnight rateLiffeLondon International Financial Futures and Options ExchangeLPILimited Price IndexLTFXLong-Term FXLVLocal VolatilityMCMonte CarloMGMetallgesellschaftMMRModified Modified RestructuringMRModified RestructuringNPNotional PrincipalNPANotional Principal AmountOFObjective FunctionOISOvernight Indexed SwapOTCOver The CounterOTMOut The MoneyPCAPrincipal Component Analysispdper dayPELPeak Exposure LimitPFEPotential Future ExposurePOTPeaks Over ThresholdPRDCPower Reverse Dual-CurrencyPVPresent ValuePV01Another name for PVBPPVBPPresent Value of 1 bpQDSQuanto Diff SwapRODRand Overnight DepositRPRobust ProgrammingSABRStochastic—αβpSONIASterling OverNight Index AverageTARNTarget Accrual Redemption NoteTRSTotal Return SwapVaRValue-at-RiskVBAVisual BAsicVCVAnother name for Delta VaRVMVariable MaturityWBWorld BankYoYYear On YearYTMYield To MaturityZARSouth African Randz-czero coupon

In memory of Marilyn, 1948 to 2003

Chapter 1

Swaps and Other Derivatives

This is the second edition. Much has changed since the first was written in 2000. For the first seven years of the new century, the derivative market continued to grow at an exponential pace. From 2008, its growth reversed, albeit not by much, as the global economic recession bit. In terms of notional amount, it reduced by just over 13% in the second half of 2008, to just under USD600 trillion. Between the publication of the first edition and the writing of the second, there have been some major developments. Two in particular stand out: the growth in the credit transfer market, and the massive issuance of complex securities enabling investors to earn potentially higher returns by taking on more risks.1 Hence the requirement for a second edition, which addresses both of these topics in considerable detail.

1.1 INTRODUCTION

In the 1970s there was an active Parallel Loan market. This arose during a period of exchange controls in Europe. Imagine that there is a UK company that needs to provide its US subsidiary with $100 million. The subsidiary is not of sufficiently good credit standing to borrow the money from a US bank without paying a considerable margin. The parent however cannot borrow the dollars itself and then pass them on to its subsidiary, or provide a parent guarantee, without being subject to the exchange control regulations which may make the transaction impossible or merely extremely expensive.

The Parallel Loan market requires a friendly US company prepared to provide the dollars, and at the same time requiring sterling in the UK, perhaps for its own subsidiary. Two loans with identical maturities are created in the two countries as shown. Usually the two principals would be at the prevailing spot FX rate, and the interest levels at the market rates. Obviously credit is a major concern, which would be alleviated by a set-off clause. This clause allowed each party to off-set unpaid receipts against payments due. As the spot and interest rates moved, one party would find that their loan would be “cheap”, i.e. below the current market levels, whilst the other would find their loan “expensive”. If the parties marked the loans to market—in other words, valued the loans relative to the current market levels—then the former would have a positive value and the latter a negative one. A “topping-up” clause, similar in today’s market to a regular mark-to-market and settlement, would often be used to call for adjustments in the principals if the rates moved by more than a trigger amount.

As exchange controls were abolished, the Parallel Loan became replaced with the back-to-back Loan market whereby the two parent organisations would enter into the loans directly with each other. This simplified the transactions, and reduced the operational risks. Because these loans were deemed to be separate transactions, albeit with an off-setting clause, they appeared on both sides of the balance sheet, with a potential adverse effect on the debt/equity ratios.

The economic driving force behind back-to-back loans is an extremely important concept called “comparative advantage”. Suppose the UK company is little known in the US; it would be expensive to raise USD directly. Therefore borrowing sterling and doing a back-to-back loan with a US company (who may of course be in exactly the reverse position) is likely to be cheaper. In theory, comparative advantage cannot exist in efficient markets; in reality, markets are not efficient but are racked by varieties of distortions. Consider the simple corporate tax system: if a company is profitable, it has to pay tax; if a company is unprofitable, it doesn’t. The system is asymmetric; unprofitable companies do not receive “negative” tax (except possibly in the form of off-sets against future profits). Any asymmetry is a distortion, and it is frequently feasible to derive mechanisms to exploit it—such as the leasing industry.

Cross-currency swaps were rapidly developed from back-to-back loans in the late 1970s. In appearance they are very similar, and from an outside observer only able to see the cashflows, identical. But subtly different in that all cashflows are described as contingent sales or purchases, i.e. each sale is contingent upon the counter-sale. These transactions, being forward conditional commitments, are off-balance sheet. We have the beginning of the OTC swap market!

The structure of a generic (or vanilla) cross-currency swap is therefore:

initial exchange of principal amounts;periodic exchanges of interest payments;2re-exchange of the principal amounts at maturity.

Notice that, if the first exchange is done at the current spot exchange rate, then it possesses no economic value and can be omitted.

Interest rate, or single-currency swaps, followed soon afterwards. Obviously exchange of principals in the same currency makes no economic sense, and hence an interest swap only consists of the single stage:

periodic exchanges of interest payments;

where interest is calculated on different reference rates. The most common form is with one side using a variable (or floating) rate which is determined at regular intervals, and the other a fixed reference rate throughout the lifetime of the swap.

1.2 APPLICATIONS OF SWAPS

As suggested by its origins, the earliest applications of the swap market were to assist in the raising of cheap funds through the comparative advantage concept. The EIB-TVA transaction in 1996 was a classic example of this, and is described in the box below. The overall benefit to the two parties was about $3 million over a 10-year period, and therefore they were both willing to enter into the swap.

Comparative Advantage:

European Investment Bank-Tennessee Valley Authority swap

Date: September 1996

Both counterparties had the same objective: to raise cheap funds. The EIB, being an European lender, wanted deutschmarks. The TVA, all of whose revenues and costs were in USD, wanted to borrow dollars. Their funding costs (expressed as a spread over the appropriate government bond market) are shown in the matrix below:

 USDDEMEIBT + 17B + 13TVAT + 24B + 17Spread7 bp4 bp

Whilst both organisations were AAA, the EIB was deemed to be the slightly better credit.

If both organisations borrowed directly in their required currency, the total funding cost would be (approximately—because strictly the spreads in different currencies are not additive) 37 bp over the two bond curves.

However, the relative spread is much closer in DEM than it is in USD. This was for two reasons:

the TVA had always borrowed USD, and hence was starting to pay the price of excess supply;it had never borrowed DEM, hence there was a considerable demand from European investors at a lower rate.

The total cost if the TVA borrowed DEM and the EIB borrowed USD would be only 34 bp, saving 3 bp pa.

The end result:

EIB issued a 10-year $1 billion bond;TVA issued a 10-year DM1.5 billion bond; andthey swapped the proceeds to raise cheaper funding, saving roughly $3 million over the 10 years.

This was a real exercise in Comparative Advantage; neither party wanted the currency of their bond issues, but it was cheaper to issue and then swap.

It was quickly realised that swaps, especially being off-balance sheet instruments, could also be effective in the management of both currency and interest rate medium-term risk. The commonest example is of a company who is currently paying floating interest, and who is concerned about interest rates rising in the future; by entering into an interest rate swap to pay a fixed rate and to receive a floating rate, uncertainty has been removed.

To ensure that the risk management is effective, the floating interest receipts under the swap must exactly match the interest payments under the debt. Therefore the swap must mirror any structural complexities in the debt, such as principal repayment schedules, or options to repay early, and so on. Usually a swap entered into between a bank and a customer is tailored specifically for that situation. This book will provide details of many of the techniques used to structure such swaps.

A well-known and very early example of the use of swaps is the one conducted between the World Bank and IBM in August 1981—described in the box below. This swap had the reputation of kick-starting the swap market because it was performed by two extremely prestigious organisations, and received a lot of publicity which attracted many other end-users to come into the market. It was the first long-term swap done by the World Bank, who is now one of the biggest users of the swap market.

World Bank-IBM Swap

Date: August 1981

This is a simplified version of the famous swap. The two counterparties have very different objectives.

IBM had embarked upon a world-wide funding programme some years earlier, raising money inter alia in deutschmarks and Swiss francs. The money was remitted back to the US for general funding. This had created a FX exposure, because IBM had to convert USDs into DEMs and CHFs regularly to make the coupon payments. Over the years the USD had significantly strengthened, creating a gain for IBM. It now wished to lock in the gain and remove any future exposure.

The World Bank had a policy of raising money in hard currency; namely DEM, CHF and yen. It was a prolific borrower, and by 1981 was finding that its cost of funds in these currencies was rising simply through an excess supply of WB paper. Its objective, as always, was to raise cheap funds.

Salomon Brothers suggested the following transactions:

(a) The WB could still raise USD at relatively cheap rates, therefore it should issue two euro-dollar bonds:

one matched the principal and maturity of IBM’s DEM liabilities equivalent to $210 million;the other matched IBM’s Swiss franc liabilities equivalent to $80 million.Each bond had a short first period to enable the timing of all the future cashflows to match.

(b) There was a 2-week settlement period, so WB entered into a FX forward contract to:

sell the total bond proceeds of $290 million;buy the equivalent in DEM and CHF;

(c) IBM and WB entered into a two-stage swap whereby:

so that IBM converted its DEM and CHD liabilities into USD, and the WB effectively raised hard currencies at a cheap rate. Both achieved their objectives!

1.3 AN OVERVIEW OF THE SWAP MARKET

From these earliest beginnings, the swap market has grown exponentially. As the graph shows, the volume of interest rate swap business now totally dominates cross-currency swaps,3 suggesting that risk management using swaps is commonplace.

The graph is shown in terms of notional principal outstanding, i.e. the principals of all swaps transacted but not yet matured; for the cross-currency swap described above, this would be recorded as [$100m + £60m * S]/2 where S is the current spot rate. The market has shown a remarkable and consistent growth in activity.

It is arguable whether this is a very appropriate way of describing the current size of the market, although it certainly attracts headlines. Many professionals would use “gross market value” or total replacement cost of all contracts as a more realistic measure. This measure had been in broad decline as banks improve their risk management, and are unwilling to take on greater risks due to the imposition of capital charges. However, as can be seen from the figures below, the gross value increased in the second half of 2008, especially in interest rate and credit derivatives, due to the dramatic movements in these markets.

A brief overview of the OTC derivative market is shown in the table below. Probably the most important statistic is that, despite all the publicity given to more exotic transactions, the overwhelming workhorse of this market is the relatively short-term interest rate swap.

The derivative markets continue to grow at an astounding rate—why? There are two main sources of growth—breadth and depth:

financial markets around the world have increasingly deregulated over the past 30 years, witness activities in Greece and Portugal, the Far East and Eastern Europe. As they do, cash and bond markets first develop followed rapidly by swap and option markets;the original swaps were done in relatively large principal amounts with high-credit counterparties. Banks have however been increasingly pushing derivatives down into the lower credit depths in the search of return. It is feasible to get quite small transactions, and some institutions even specialise in aggregating retail demand into a wholesale transaction.

A brief overview of the current state of the derivative market (in December 2008) (extracted from the semiannual BIS surveys)

The total OTC derivative market was estimated to be just under $600 trillion, measured in terms of outstanding principal amount, broken up as shown below (in US billions):

The table shows the fairly dramatic slowdown and then drop during 2008, especially with equity, commodity and credit-related derivatives, but also the increase in gross value.

MaturityFXIRSUnder 1 year65%33% of total market1-5 years19%33%Over 5 years16%34%

The above table shows that the majority of FX derivatives, predominantly forwards, are under 1 year in maturity, interest rate derivatives are typically much longer, averaging between 5 and 10 years. The Eurozone, UK and US routinely now trade swaps out to 50 years. In terms of currencies, the major ones have little changed over the past 10 years. The main development is the increased rise in euro products, and the relative decline in USD.

CurrencyPercentage of market share of IR derivatives Dec-08USD36.6%Euro38.7Yen14.1GBP7.4Sw Fr1.2Can $0.7Sw Kr1.3

1.4 THE EVOLUTION OF THE SWAP MARKET

The discussion below refers to the evolution of the early swap market in the major currencies during the 1980s. It is however applicable to many other generic markets as they have developed.

There are typically three phases of development of a swap market:

1. In the earliest days of a market, it is very much an arranged market whereby two swap end-users would negotiate directly with each other, and an “advisory” bank may well extract an upfront fee for locating and assisting them. This was obviously a slow market, with documentation frequently tailored for each transaction. The main banks involved are investment or merchant banks, long on people but low on capital and technology as of course they were taking no risk. Typical counterparties would be highly rated, and therefore happy to deal directly with each other.

The first swap markets in the major currencies were even slower, as there was considerable doubt about the efficacy of swaps. End-users were dubious about moving the activities off-balance sheet, and there was apprehension that the accounting rules would be changed to force them back on-balance sheet. The World Bank-IBM swap (described above) played a major role in persuading people that the swap market was acceptable.

2. In the second phase, originally early to mid-1980s, commercial banks started to take an increasing role providing traditional credit guarantees.

The counterparties now would both negotiate directly with the bank, who would structure back-to-back swaps but take the credit risk, usually for an on-going spread not an upfront fee. The normal lending departments of the bank would be responsible for negotiating the transaction and the credit spread. The documentation is now more standardised and provided by the bank. This role is often described as acting as an “intermediary”, taking credit but not market risk.

The role of intermediary may also be encouraged by external legislation. In the UK for example, if a swap is entered into by two non-bank counterparties, the cashflows are subject to withholding tax. This is not true if one counterparty is a bank.

3.