Understanding Credit Derivatives and Related Instruments ThisPageIntentionallyLeftBlank. Understanding Credit Derivatives and Related Instruments Antulio N. Bomfim Amsterdam • Boston • Heidelberg • London • New York • Oxford Paris • San Diego • San Francisco • Singapore • Sydney • Tokyo Elsevier Academic Press 525 B Street, Suite 1900, San Diego, California 92101-4495, USA 84 Theobald’s Road, London WC1X 8RR, UK This book is printed on acid-free paper. Copyright c 2005, Elsevier Inc. All rights reserved. Disclaimer: The analysis and conclusions set out in this book are the author’s own, the author is solely responsible for its content. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. 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Contents I Credit Derivatives: Definition, Market, Uses 1 1 Credit Derivatives: A Brief Overview ............ 3 1.1WhatareCreditDerivatives?................. 3 1.2Potential“GainsfromTrade”................ 5 1.3TypesofCreditDerivatives.................. 6 1.3.1 Single-NameInstruments............... 6 1.3.2 Multi-NameInstruments............... 7 1.3.3 Credit-Linked Notes .................. 8 1.3.4 Sovereignvs.OtherReferenceEntities........ 8 1.4ValuationPrinciples...................... 9 1.4.1 Fundamental Factors ................. 10 1.4.2 OtherPotentialRiskFactors............. 11 1.4.3 Static Replication vs. Modeling ............ 12 1.4.4 A Note on Supply, Demand, and Market Frictions . 14 1.5 Counterparty Credit Risk (Again) .............. 15 2 The Credit Derivatives Market ................ 17 2.1EvolutionandSizeoftheMarket............... 18 2.2 Market Activity and Size by Instrument Type ........ 19 2.2.1 Single-vs.Multi-nameInstruments......... 20 2.2.2 Sovereignvs.OtherReferenceEntities........ 21 viii Contents 2.2.3 CreditQualityofReferenceEntities......... 21 2.2.4 Maturities of Most Commonly Negotiated Contracts ................. 23 2.3MainMarketParticipants................... 23 2.3.1 BuyersandSellersofCreditProtection....... 24 2.4CommonMarketPractices.................. 25 2.4.1 A First Look at Documentation Issues ........ 26 2.4.2 CollateralizationandNetting............. 27 3 Main Uses of Credit Derivatives ............... 29 3.1CreditRiskManagementbyBanks............. 29 3.2 Managing Bank Regulatory Capital ............. 31 3.2.1 A Brief Digression: The 1988 Basle Accord ..... 31 3.2.2 Credit Derivatives and Regulatory CapitalManagement................. 33 3.3 Yield Enhancement, Portfolio Diversification ........ 35 3.3.1 Leveraging Credit Exposure, Unfunded Instruments ................ 35 3.3.2 Synthesizing Long Positions inCorporateDebt................... 36 3.4ShortingCorporateBonds.................. 37 3.5OtherUsesofCreditDerivatives............... 38 3.5.1 HedgingVendor-financedDeals............ 38 3.5.2 HedgingbyConvertibleBondInvestors....... 38 3.5.3 Selling Protection as an Alternative to Loan Origination .................. 39 3.6 Credit Derivatives as Market Indicators ........... 39 II Main Types of Credit Derivatives 41 4 Floating-Rate Notes ....................... 43 4.1NotaCreditDerivative...................... 43 4.2HowDoesItWork?...................... 43 4.3CommonUses......................... 45 4.4ValuationConsiderations................... 45 5 Asset Swaps ............................ 53 5.1ABorderlineCreditDerivative.................. 53 5.2HowDoesItWork?...................... 54 5.3CommonUses......................... 56 5.4ValuationConsiderations................... 58 5.4.1 Valuing the Two Pieces of an Asset Swap ...... 59 5.4.2 Comparison to Par Floaters .............. 62 Contents ix 6 Credit Default Swaps ...................... 67 6.1HowDoesItWork?...................... 68 6.2CommonUses......................... 70 6.2.1 ProtectionBuyers................... 70 6.2.2 ProtectionSellers................... 71 6.2.3 SomeAdditionalExamples.............. 72 6.3ValuationConsiderations................... 73 6.3.1 CDSvs.CashSpreadsinPractice.......... 76 6.3.2 ACloserLookattheCDS-CashBasis........ 78 6.3.3 WhenCashSpreadsareUnavailable........... 80 6.4VariationsontheBasicStructure.............. 82 7 Total Return Swaps ....................... 83 7.1HowDoesItWork?...................... 83 7.2CommonUses......................... 85 7.3ValuationConsiderations................... 87 7.4VariationsontheBasicStructure.............. 89 8 Spread and Bond Options ................... 91 8.1HowDoesItWork?...................... 91 8.2CommonUses......................... 93 8.3ValuationConsiderations................... 95 8.4VariationsonBasicStructures................ 96 9 Basket Default Swaps ...................... 99 9.1HowDoesItWork?...................... 99 9.2CommonUses......................... 101 9.3ValuationConsiderations................... 101 9.3.1 AFirstLookatDefaultCorrelation......... 104 9.4VariationsontheBasicStructure.............. 105 10 Portfolio Default Swaps .....................107 10.1HowDoesItWork?...................... 107 10.2CommonUses......................... 110 10.3ValuationConsiderations................... 110 10.3.1 A First Look at the Loss Distribution Function . 111 10.3.2LossDistributionandDefaultCorrelation...... 113 10.4VariationsontheBasicStructure.............. 116 11 Principal-Protected Structures ................117 11.1HowDoesItWork?...................... 117 11.2CommonUses......................... 119 11.3ValuationConsiderations................... 119 11.4VariationsontheBasicStructure.............. 122 x Contents 12 Credit-Linked Notes .......................123 12.1HowDoesItWork?...................... 123 12.2CommonUses......................... 125 12.3ValuationConsiderations................... 126 12.4VariationsontheBasicStructure.............. 126 13 Repackaging Vehicles ......................127 13.1HowDoesItWork?...................... 127 13.2WhyUseRepackagingVehicles?............... 129 13.3ValuationConsiderations................... 130 13.4VariationsontheBasicStructure.............. 130 14 Synthetic CDOs .........................133 14.1TraditionalCDOs....................... 133 14.1.1HowDoesItWork?.................. 134 14.1.2 Common Uses: Balance-sheet and ArbitrageCDOs.................... 136 14.1.3ValuationConsiderations............... 137 14.2SyntheticSecuritization.................... 137 14.2.1CommonUses:WhyGoSynthetic?......... 139 14.2.2ValuationConsiderationsforSyntheticCDOs....140 14.2.3VariationsontheBasicStructure.......... 140 III Introduction to Credit Modeling I: Single-Name Defaults 143 15 Valuing Defaultable Bonds ...................145 15.1Zero-couponBonds...................... 145 15.2 Risk-neutral Valuation and Probability ........... 147 15.2.1 Risk-neutral Probabilities ............... 149 15.3Coupon-payingBonds..................... 150 15.4NonzeroRecovery....................... 152 15.5RiskyBondSpreads...................... 153 15.6 Recovery Rates ........................ 154 16 The Credit Curve ........................157 16.1CDS-impliedCreditCurves.................. 158 16.1.1 Implied Survival Probabilities ............ 159 16.1.2Examples........................161 16.1.3FlatCDSCurveAssumption............. 162 16.1.4ASimpleRuleofThumb............... 163 16.1.5 Sensitivity to Recovery Rate Assumptions ...... 164 16.2MarkingtoMarketaCDSPosition............. 164 Contents xi 16.3 Valuing a Principal-protected Note .............. 166 16.3.1Examples........................167 16.3.2 PPNs vs. Vanilla Notes ................ 168 16.4OtherApplicationsandSomeCaveats............ 169 17 Main Credit Modeling Approaches ..............171 17.1StructuralApproach..................... 172 17.1.1TheBlack-Scholes-MertonModel........... 172 17.1.2 Solving the Black-Scholes-Merton Model ....... 176 17.1.3 Practical Implementation of the Model ....... 178 17.1.4ExtensionsandEmpiricalValidation......... 178 17.1.5CreditDefaultSwapValuation............ 181 17.2Reduced-formApproach................... 183 17.2.1OverviewofSomeImportantConcepts........183 17.2.1.1 Stochastic Interest Rates .......... 184 17.2.1.2 Forward Default Probabilities