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Credit Derivatives
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Table of Contents

Preface to the First Edition xvii Preface to the Second Edition xix Acknowledgements xxi Disclaimer xxiii Table of Spreadsheet Examples and Software xxvii About the Author xxix PART I CREDIT BACKGROUND AND CREDIT DERIVATIVES 1 1 Credit Debt and Other Traditional Credit Instruments 3 1.1 Bonds and Loans; Libor Rates and Swaps; 'REPO' and General Collateral Rates 3 1.2 Credit Debt Versus 'Risk-Free' Debt 6 1.3 Issue Documents, Seniority and the Recovery Process 6 1.4 Valuation, Yield and Spread 10 1.5 Buying Risk 10 1.6 Marking to Market, Marking to Model and Reserves 11 1.7 The 'Credit Crunch' and Correlation 12 1.8 Parties Involved in the Credit Markets and Key Terminology 13 2 Default and Recovery Data; Transition Matrices; Historical Pricing 15 2.1 Recovery: Ultimate and Market-Value-Based Recovery 15 2.2 Default Rates: Rating and Other Factors 21 2.3 Transition Matrices 21 2.4 'Measures' and Transition Matrix-Based Pricing 22 2.5 Spread Jumps and Spread Volatility Derived from Transition Matrices 26 2.6 Adjusting Transition Matrices 27 3 Asset Swaps and Asset Swap Spread; z-Spread 29 3.1 'Par-Par' Asset Swap Contracts 29 3.2 Asset Swap Spread 30 3.3 Maturity and z-Spread 30 3.4 Callable Asset Swaps; 'Perfect' Asset Swaps 32 3.5 A Bond Spread Model 33 4 Liquidity, the Credit Pyramid and Market Data 35 4.1 Bond Liquidity 35 4.2 The Credit Pyramid 35 4.3 Engineered and Survey Data 37 4.4 Spread and Rating 39 5 Traditional Counterparty Risk Management 41 5.1 Vetting 41 5.2 Collateralisation and Netting 41 5.3 Additional Counterparty Requirements for Credit Derivative Counterparties 42 5.4 Internal Capital Charge 42 6 Credit Portfolios and Portfolio Risk 43 6.1 VaR and counterpartyVaR 43 6.2 Distribution of Forward Values of a Credit Bond 43 6.3 Correlation and the Multi-Factor Normal (Gaussian) Distribution 45 6.4 Correlation and the Correlation Matrix 46 7 Introduction to Credit Derivatives 49 7.1 Products and Users 49 7.2 Market Participants and Market Growth 51 PART II CREDIT DEFAULT SWAPS AND OTHER SINGLE NAME PRODUCTS 55 8 Credit Default Swaps; Product Description and Simple Applications 57 8.1 CDS Product Definition 57 8.2 Documentation 60 8.3 Credit Triggers for Credit Derivatives 65 8.4 CDS Applications and Elementary Strategies 67 8.5 Counterparty Risk: PFE for CDS 71 8.6 CDS Trading Desk 71 8.7 CDS Contract and Convention Changes 2009 73 9 Valuation and Risk: Basic Concepts and the Default and Recovery Model 81 9.1 The Fundamental Credit Arbitrage ? Repo Cost 81 9.2 Default and Recovery Model; Claim Amount 82 9.3 Deterministic Default Rate Model 87 9.4 Stochastic Default Rate Model; Hazard and Pseudo-Hazard Rates 94 9.5 Calibration to Market Data 97 9.6 CDS Data/Sources 102 9.7 Model Errors and Tests 105 9.8 CDS Risk Factors; Reserves and Model Risk 108 10 CDS Deal Examples 113 10.1 A CDS Hedged Against Another CDS 113 10.2 Introduction to Bond Hedging 124 10.3 Hedge and Credit Event Examples 126 11 CDS/Bond Basis Trading 131 11.1 Bond Versus CDS: Liquidity 131 11.2 Bond Repo Cost 132 11.3 Bond Spread Measurement ? z-Spread not Asset Swap Spread 133 11.4 Bond Price Impact 133 11.5 Embedded Options in Bonds and Loans 134 11.6 Delivery Option in CDSs 135 11.7 Payoff of Par 136 11.8 Trigger Event Differences 136 11.9 Embedded Repo Option 137 11.10 Putting it All Together 138 12 Forward CDS; Back-to-Back CDS, Mark to Market and CDS Unwind 139 12.1 Forward CDS 139 12.2 Mark-to-Market and Back-to-Back CDS 140 12.3 Unwind Calculation; Off-Market Trade Valuation and Hedging 141 12.4 'Double-Trigger CDS' 142 13 Credit-Linked Notes 145 13.1 CLN Set-Up; Counterparty or Collateral Risk 145 13.2 Embedded Swaps and Options 147 13.3 Costs 148 13.4 Applications 148 13.5 CLN Pricing 149 13.6 Capital Guaranteed Note 150 14 Digital or 'Fixed Recovery' CDS 155 14.1 Product Description 155 14.2 Pricing, Hedging, Valuation and Risk Calculations 155 14.3 Trigger Event Differences 157 15 Spread Options, Callable/Puttable Bonds, Callable Asset Swaps, Callable Default Swaps 159 15.1 Product Definitions 159 15.2 Model Alternatives and a Stochastic Default Rate Model for Spread Option Pricing 162 15.3 Sensitivities and Hedging 164 16 Total Return Swaps 167 16.1 Product Definition and Examples 167 16.2 Applications 167 16.3 Hedging and Valuation 168 17 Single Name Book Management 171 17.1 Risk Aggregation 171 17.2 CreditVaR for CDSs 173 18 CDS and Simulation 175 18.1 The Poisson Model and Default Times 175 18.2 Valuation by Monte Carlo Simulation 175 18.3 Sensitivity 178 PART III PORTFOLIO PRODUCTS 181 19 Portfolio Product Types 183 19.1 Nth-to-Default Baskets 184 19.2 'Synthetic' CDOs 188 19.3 Cashflow CDOs 210 19.4 Credit Securitisations 220 19.5 Rating 222 19.6 Alternative Levered Credit Portfolio Products 222 20 The Normal Copula and Correlation 227 20.1 Default Time Correlation 227 20.2 Normal Copula 236 20.3 Correlation 244 21 Correlation in Practice 253 21.1 Tranche Correlation 253 21.2 Base Correlation 257 21.3 Correlated Recoveries 261 21.4 Correlation Regime Change and Other Modelling Approaches 262 22 Valuation and Hedging 265 22.1 Valuation Examples 265 22.2 Sensitivity Calculation and Hedging 270 22.3 Pricing More Complex Structures 282 22.4 Model Errors and Tests; Alternative Models 284 23 Alternative Copulas 289 23.1 Student's t-Distribution 289 23.2 Copulas in General 290 23.3 Archimedean Copulas: Clayton, Gumbel 291 23.4 Clayton at theta = 0 and theta = infinity 293 23.5 Model Risk 293 24 Correlation Portfolio Management 297 24.1 Static and Dynamic Hedges 297 24.2 Correlation Book Management 298 24.3 CreditVaR and CounterpartyVaR 300 PART IV DEFAULT SWAPS INCLUDING COUNTERPARTY RISK 303 25 Single Name CDS 303 25.1 Non-Correlated Counterparty 305 25.2 100% Correlation 306 25.3 Correlated Counterparty: Pricing and Hedging 308 25.4 Choice of Copula 309 25.5 Collateralised Deals and CDS Book Management 309 26 Counterparty CDSs 313 26.1 Pricing 313 26.2 Counterparty CDS (CCDS) Book Management 313 PART V SYSTEMS IMPLEMENTATION AND TESTING 317 27 Mathematical Model and Systems Validation 319 27.1 Testing Procedures 319 27.2 Implementation and Documentation 321 28 System Implementation 323 28.1 Anatomy of a CDO 323 28.2 Management 325 28.3 Valuation 329 28.4 IT Considerations 331 PART VI THE CREDIT CRISIS 335 29 Cause and Effect: Credit Derivatives and the Crisis of 2007 337 29.1 The Credit Markets Pre-Crisis 337 29.2 The Events of MID-2007 341 29.3 Issues to be Addressed 346 29.4 Market Clearing Mechanisms 350 Appendix Markit Credit and Loan Indices 355 References 363 Index 365

About the Author

GEOFF CHAPLIN studied mathematics at Cambridge (MA 1972) and Oxford (MSc 1973, DPhil 1975) and trained as an actuary (FFA 1978) while working in a life insurance company. He moved to the City in 1980 and has worked for major banks (including HSBC, Nomura International, and ABN AMRO). As a partner in Reoch Credit he has consulted to law firms, hedge funds, corporate treasurers, institutional investment funds and risk control departments of major banks in the areas of credit and mortality risk. He has been involved in the credit derivatives market since 1996 and life settlements structures since 2003. Geoff has also maintained strong academic interests ? he was a visiting (emeritus) professor at the University of Waterloo, Canada, from 1987 until 1999. He has also published many articles in Risk, the Journal of the Institute and Faculty of Actuaries, and others, speaks regularly at conferences and is the author of Credit Derivatives: Risk Management, Trading and Investing (John Wiley & Sons Ltd, 2005) and co-author of Life Settlements and Longevity Structures: Pricing and Risk Management: Investment and Structured Finance (John Wiley & Sons Ltd, 2009).

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