Credit Derivatives: Trading, Investing, and Risk Management, 2nd Edition

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