O'Kane | Modelling Single-name and Multi-name Credit Derivatives | Buch | 978-0-470-51928-8 | www.sack.de

Buch, Englisch, 512 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 1056 g

Reihe: Wiley Finance Series

O'Kane

Modelling Single-name and Multi-name Credit Derivatives


1. Auflage 2008
ISBN: 978-0-470-51928-8
Verlag: Wiley

Buch, Englisch, 512 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 1056 g

Reihe: Wiley Finance Series

ISBN: 978-0-470-51928-8
Verlag: Wiley


Modelling Single-name and Multi-name Credit Derivatives presents an up-to-date, comprehensive, accessible and practical guide to the pricing and risk-management of credit derivatives. It is both a detailed introduction to credit derivative modelling and a reference for those who are already practitioners.

This book is up-to-date as it covers many of the important developments which have occurred in the credit derivatives market in the past 4-5 years. These include the arrival of the CDS portfolio indices and all of the products based on these indices. In terms of models, this book covers the challenge of modelling single-tranche CDOs in the presence of the correlation skew, as well as the pricing and risk of more recent products such as constant maturity CDS, portfolio swaptions, CDO squareds, credit CPPI and credit CPDOs.

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Weitere Infos & Material


Acknowledgements xiii

About the Author xv

Introduction vii

Notation xix

1 The Credit Derivatives Market 1

1.1 Introduction 1

1.2 Market Growth 2

1.3 Products 4

1.4 Market Participants 6

1.5 Summary 7

2 Building the Libor Discount Curve 9

2.1 Introduction 9

2.2 The Libor Index 9

2.3 Money Market Deposits 10

2.4 Forward Rate Agreements 12

2.5 Interest Rate Futures 13

2.6 Interest Rate Swaps 16

2.7 Bootstrapping the Libor Curve 21

2.8 Summary 26

2.9 Technical Appendix 26

Part I Single-name Credit Derivatives 29

3 Single-name Credit Modelling 31

3.1 Introduction 31

3.2 Observing Default 32

3.3 Risk-neutral Pricing Framework 35

3.4 Structural Models of Default 38

3.5 Reduced Form Models 42

3.6 The Hazard Rate Model 44

3.7 Modelling Default as a Cox Process 46

3.8 A Gaussian Short Rate and Hazard Rate Model 49

3.9 Independence and Deterministic Hazard Rates 51

3.10 The Credit Triangle 54

3.11 The Credit Risk Premium 55

3.12 Summary 57

3.13 Technical Appendix 57

4 Bonds and Asset Swaps 59

4.1 Introduction 59

4.2 Fixed Rate Bonds 60

4.3 Floating Rate Notes 68

4.4 The Asset Swap 72

4.5 The Market Asset Swap 78

4.6 Summary 80

5 The Credit Default Swap 81

5.1 Introduction 81

5.2 The Mechanics of the CDS Contract 82

5.3 Mechanics of the Premium Leg 84

5.4 Mechanics of the Protection Leg 85

5.5 Bonds and the CDS Spread 90

5.6 The CDS–Cash basis 92

5.7 Loan CDS 94

5.8 Summary 95

6 A Valuation Model for Credit Default Swaps 97

6.1 Introduction 97

6.2 Unwinding a CDS Contract 97

6.3 Requirements of a CDS Pricing Model 99

6.4 Modelling a CDS Contract 100

6.5 Valuing the Premium Leg 101

6.6 Valuing the Protection Leg 105

6.7 Upfront Credit Default Swaps 108

6.8 Digital Default Swaps 110

6.9 Valuing Loan CDS 111

6.10 Summary 112

7 Calibrating the CDS Survival Curve 113

7.1 Introduction 113

7.2 Desirable Curve Properties 113

7.3 The Bootstrap 114

7.4 Interpolation Quantities 115

7.5 Bootstrapping Algorithm 117

7.6 Behaviour of the Interpolation Scheme 118

7.7 Detecting Arbitrage in the Curve 121

7.8 Example CDS Valuation 123

7.9 Summary 125

8 CDS Risk Management 127

8.1 Introduction 127

8.2 Market Risks of a CDS Position 127

8.3 Analytical CDS Sensitivities 128

8.4 Full Hedging of a CDS Contract 138

8.5 Hedging the CDS Spread Curve Risk 139

8.6 Hedging the Libor Curve Risk 145

8.7 Portfolio Level Hedging 147

8.8 Counterparty Risk 148

8.9 Summary 149

9 Forwards, Swaptions and CMDS 151

9.1 Introduction 151

9.2 Forward Starting CDS 151

9.3 The Default Swaption 156

9.4 Constant Maturity Default Swaps 169

9.5 Summary 180

Part II Multi-name Credit Derivatives 181

10 CDS Portfolio Indices 183

10.1 Introduction 183

10.2 Mechanics of the Standard Indices 184

10.3 CDS Portfolio Index Valuation 188

10.4 The Index Curve 190

10.5 Calculating the Intrinsic Spread of an Index 192

10.6 The Portfolio Swap Adjustment 195

10.7 Asset-backed and Loan CDS Indices 200

10.8 Summary 201

11 Options on CDS Portfolio Indices 203

11.1 Introduction 203

11.2 Mechanics 203

11.3 Valuation of an Index Option 207

11.4 An Arbitrage-free Pricing Model 209

11.5 Examples of Pricing 213

11.6 Risk Management 215

11.7 Black’s Model Revisited 215

11.8 Summary 217

12 An Introduction to Correlation Products 219

12.1 Introduction 219

12.2 Default Baskets 219

12.3 Leveraging the Spread Premia 227

12.4 Collateralised Debt Obligations 230

12.5 The Single-tranche Synthetic CDO 232

12.6 CDOs and Correlation 236

12.7 The Tranche Survival Curve 237

12.8 The Standard Index Tranches 240

12.9 Summary 240

13 The Gaussian Latent Variable Model 241

13.1 Introduction 241

13.2 The Model 241

13.3 The Multi-name Latent Variable Model 243

13.4 Conditional Independence 246

13.5 Simulating Multi-name Default 248

13.6 Default Induced Spread Dynamics 253

13.7 Calibrating the Correlation 257

13.8 Summary 258

14 Modelling Default Times using Copulas 261

14.1 Introduction 261

14.2 Definition and Properties of a Copula 261

14.3 Measuring Dependence 264

14.4 Rank Correlation 265

14.5 Tail Dependence 269

14.6 Some Important Copulae 270

14.7 Pricing Credit Derivatives from Default Times 278

14.8 Standard Error of the Breakeven Spread 280

14.9 Summary 281

14.10 Technical Appendix 282

15 Pricing Default Baskets 283

15.1 Introduction 283

15.2 Modelling First-to-default Baskets 283

15.3 Second-to-default and Higher Default Baskets 291

15.4 Pricing Baskets using Monte Carlo 294

15.5 Pricing Baskets using a Multi-Factor Model 296

15.6 Pricing Baskets in the Student-t Copula 298

15.7 Risk Management of Default Baskets 299

15.8 Summary 301

16 Pricing Tranches in the Gaussian Copula Model 303

16.1 Introduction 303

16.2 The LHP Model 303

16.3 Drivers of the Tranche Spread 308

16.4 Accuracy of the LHP Approximation 312

16.5 The LHP Model with Tail Dependence 313

16.6 Summary 314

16.7 Technical Appendix 314

17 Risk Management of Synthetic Tranches 317

17.1 Introduction 317

17.2 Systemic Risks 318

17.3 The LH+ Model 324

17.4 Idiosyncratic Risks 328

17.5 Hedging Tranches 334

17.6 Summary 339

17.7 Technical Appendix 339

18 Building the Full Loss Distribution 343

18.1 Introduction 343

18.2 Calculating the Tranche Survival Curve 343

18.3 Building the Conditional Loss Distribution 345

18.4 Integrating over the Market Factor 353

18.5 Approximating the Conditional Portfolio Loss Distribution 354

18.6 A Comparison of Methods 360

18.7 Perturbing the Loss Distribution 362

18.8 Summary 364

19 Implied Correlation 365

19.1 Introduction 365

19.2 Implied Correlation 365

19.3 Compound Correlation 367

19.4 Disadvantages of Compound Correlation 370

19.5 No-arbitrage Conditions 371

19.6 Summary 374

20 Base Correlation 375

20.1 Introduction 375

20.2 Base Correlation 375

20.3 Building the Base Correlation Curve 377

20.4 Base Correlation Interpolation 382

20.5 Interpolating Base Correlation using the ETL 389

20.6 A Base Correlation Surface 393

20.7 Risk Management of Index Tranches 394

20.8 Hedging the Base Correlation Skew 395

20.9 Base Correlation for Bespoke Tranches 398

20.10 Risk Management of Bespoke Tranches 405

20.11 Summary 406

21 Copula Skew Models 409

21.1 Introduction 409

21.2 The Challenge of Fitting the Skew 409

21.3 Calibration 411

21.4 Random Recovery 412

21.5 The Student-t Copula 413

21.6 The Double-t Copula 415

21.7 The Composite Basket Model 418

21.8 The Marshall–Olkin Copula 420

21.9 The Mixing Copula 421

21.10 The Random Factor Loading Model 423

21.11 The Implied Copula 427

21.12 Copula Comparison 429

21.13 Pricing Bespokes 431

21.14 Summary 431

22 Advanced Multi-name Credit Derivatives 433

22.1 Introduction 433

22.2 Credit CPPI 433

22.3 Constant Proportion Debt Obligations 436

22.4 The CDO-squared 441

22.5 Tranchelets 448

22.6 Forward Starting Tranches 449

22.7 Options on Tranches 449

22.8 Leveraged Super Senior 450

22.9 Summary 451

23 Dynamic Bottom-up Correlation Models 453

23.1 Introduction 453

23.2 A Survey of Dynamic Models 455

23.3 The Intensity Gamma Model 458

23.4 The Affine Jump Diffusion Model 466

23.5 Summary 470

23.6 Technical Appendix 470

24 Dynamic Top-down Correlation Models 471

24.1 Introduction 471

24.2 The Markov Chain Approach 472

24.3 Markov Chain: Initial Generator 474

24.4 Markov Chain: Stochastic Generator 479

24.5 Summary 483

Appendix A Useful Formulae 485

Bibliography 487

Index 491


Dominic O'Kane is an affiliated Professor of Finance at the French business school EDHEC which is based in Nice, France. Until May 2006, Dominic O'Kane was a managing director and ran the European Fixed Income Quantitative Research group at Lehman Brothers, the US investment bank. Dominic spent seven of his nine years at Lehman Brothers working as a quant for the credit derivatives trading desk.



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