What is included with this book?
Acknowledgements | p. xiii |
About the Author | p. xv |
Introduction | p. xvii |
Notation | p. xix |
The Credit Derivatives Market | p. 1 |
Introduction | p. 1 |
Market Growth | p. 2 |
Products | p. 4 |
Market Participants | p. 6 |
Summary | p. 7 |
Building the Libor Discount Curve | p. 9 |
Introduction | p. 9 |
The Libor Index | p. 9 |
Money Market Deposits | p. 10 |
Forward Rate Agreements | p. 12 |
Interest Rate Futures | p. 13 |
Interest Rate Swaps | p. 16 |
Bootstrapping the Libor Curve | p. 21 |
Summary | p. 26 |
Technical Appendix | p. 26 |
Single-Name Credit Derivatives | p. 29 |
Single-name Credit Modelling | p. 31 |
Introduction | p. 31 |
Observing Default | p. 32 |
Risk-neutral Pricing Framework | p. 35 |
Structural Models of Default | p. 38 |
Reduced Form Models | p. 42 |
The Hazard Rate Model | p. 44 |
Modelling Default as a Cox Process | p. 46 |
A Gaussian Short Rate and Hazard Rate Model | p. 49 |
Independence and Deterministic Hazard Rates | p. 51 |
The Credit Triangle | p. 54 |
The Credit Risk Premium | p. 55 |
Summary | p. 57 |
Technical Appendix | p. 57 |
Bonds and Asset Swaps | p. 59 |
Introduction | p. 59 |
Fixed Rate Bonds | p. 60 |
Floating Rate Notes | p. 68 |
The Asset Swap | p. 72 |
The Market Asset Swap | p. 78 |
Summary | p. 80 |
The Credit Default Swap | p. 81 |
Introduction | p. 81 |
The Mechanics of the CDS Contract | p. 82 |
Mechanics of the Premium Leg | p. 84 |
Mechanics of the Protection Leg | p. 85 |
Bonds and the CDS Spread | p. 90 |
The CDS-Cash basis | p. 92 |
Loan CDS | p. 94 |
Summary | p. 95 |
A Valuation Model for Credit Default Swaps | p. 97 |
Introduction | p. 97 |
Unwinding a CDS Contract | p. 97 |
Requirements of a CDS Pricing Model | p. 99 |
Modelling a CDS Contract | p. 100 |
Valuing the Premium Leg | p. 101 |
Valuing the Protection Leg | p. 105 |
Upfront Credit Default Swaps | p. 108 |
Digital Default Swaps | p. 110 |
Valuing Loan CDS | p. 111 |
Summary | p. 112 |
Calibrating the CDS Survival Curve | p. 113 |
Introduction | p. 113 |
Desirable Curve Properties | p. 113 |
The Bootstrap | p. 114 |
Interpolation Quantities | p. 115 |
Bootstrapping Algorithm | p. 117 |
Behaviour of the Interpolation Scheme | p. 118 |
Detecting Arbitrage in the Curve | p. 121 |
Example CDS Valuation | p. 123 |
Summary | p. 125 |
CDS Risk Management | p. 127 |
Introduction | p. 127 |
Market Risks of a CDS Position | p. 127 |
Analytical CDS Sensitivities | p. 128 |
Full Hedging of a CDS Contract | p. 138 |
Hedging the CDS Spread Curve Risk | p. 139 |
Hedging the Libor Curve Risk | p. 145 |
Portfolio Level Hedging | p. 147 |
Counterparty Risk | p. 148 |
Summary | p. 149 |
Forwards, Swaptions and CMDS | p. 151 |
Introduction | p. 151 |
Forward Starting CDS | p. 151 |
The Default Swaption | p. 156 |
Constant Maturity Default Swaps | p. 169 |
Summary | p. 180 |
Multi-Name Credit Derivatives | p. 181 |
CDS Portfolio Indices | p. 183 |
Introduction | p. 183 |
Mechanics of the Standard Indices | p. 184 |
CDS Portfolio Index Valuation | p. 188 |
The Index Curve | p. 190 |
Calculating the Intrinsic Spread of an Index | p. 192 |
The Portfolio Swap Adjustment | p. 195 |
Asset-backed and Loan CDS Indices | p. 200 |
Summary | p. 201 |
Options on CDS Portfolio Indices | p. 203 |
Introduction | p. 203 |
Mechanics | p. 203 |
Valuation of an Index Option | p. 207 |
An Arbitrage-free Pricing Model | p. 209 |
Examples of Pricing | p. 213 |
Risk Management | p. 215 |
Black's Model Revisited | p. 215 |
Summary | p. 217 |
An Introduction to Correlation Products | p. 219 |
Introduction | p. 219 |
Default Baskets | p. 219 |
Leveraging the Spread Premia | p. 227 |
Collateralised Debt Obligations | p. 230 |
The Single-tranche Synthetic CDO | p. 232 |
CDOs and Correlation | p. 236 |
The Tranche Survival Curve | p. 237 |
The Standard Index Tranches | p. 240 |
Summary | p. 240 |
The Gaussian Latent Variable Model | p. 241 |
Introduction | p. 241 |
The Model | p. 241 |
The Multi-name Latent Variable Model | p. 243 |
Conditional Independence | p. 246 |
Simulating Multi-name Default | p. 248 |
Default Induced Spread Dynamics | p. 253 |
Calibrating the Correlation | p. 257 |
Summary | p. 258 |
Modelling Default Times using Copulas | p. 261 |
Introduction | p. 261 |
Definition and Properties of a Copula | p. 261 |
Measuring Dependence | p. 264 |
Rank Correlation | p. 265 |
Tail Dependence | p. 269 |
Some Important Copulae | p. 270 |
Pricing Credit Derivatives from Default Times | p. 278 |
Standard Error of the Breakeven Spread | p. 280 |
Summary | p. 281 |
Technical Appendix | p. 282 |
Pricing Default Baskets | p. 283 |
Introduction | p. 283 |
Modelling First-to-default Baskets | p. 283 |
Second-to-default and Higher Default Baskets | p. 291 |
Pricing Baskets using Monte Carlo | p. 294 |
Pricing Baskets using a Multi-Factor Model | p. 296 |
Pricing Baskets in the Student-t Copula | p. 298 |
Risk Management of Default Baskets | p. 299 |
Summary | p. 301 |
Pricing Tranches in the Gaussian Copula Model | p. 303 |
Introduction | p. 303 |
The LHP Model | p. 303 |
Drivers of the Tranche Spread | p. 308 |
Accuracy of the LHP Approximation | p. 312 |
The LHP Model with Tail Dependence | p. 313 |
Summary | p. 314 |
Technical Appendix | p. 314 |
Risk Management of Synthetic Tranches | p. 317 |
Introduction | p. 317 |
Systemic Risks | p. 318 |
The LH+ Model | p. 324 |
Idiosyncratic Risks | p. 328 |
Hedging Tranches | p. 334 |
Summary | p. 339 |
Technical Appendix | p. 339 |
Building the Full Loss Distribution | p. 343 |
Introduction | p. 343 |
Calculating the Tranche Survival Curve | p. 343 |
Building the Conditional Loss Distribution | p. 345 |
Integrating over the Market Factor | p. 353 |
Approximating the Conditional Portfolio Loss Distribution | p. 354 |
A Comparison of Methods | p. 360 |
Perturbing the Loss Distribution | p. 362 |
Summary | p. 364 |
Implied Correlation | p. 365 |
Introduction | p. 365 |
Implied Correlation | p. 365 |
Compound Correlation | p. 367 |
Disadvantages of Compound Correlation | p. 370 |
No-arbitrage Conditions | p. 371 |
Summary | p. 374 |
Base Correlation | p. 375 |
Introduction | p. 375 |
Base Correlation | p. 375 |
Building the Base Correlation Curve | p. 377 |
Base Correlation Interpolation | p. 382 |
Interpolating Base Correlation using the ETL | p. 389 |
A Base Correlation Surface | p. 393 |
Risk Management of Index Tranches | p. 394 |
Hedging the Base Correlation Skew | p. 395 |
Base Correlation for Bespoke Tranches | p. 398 |
Risk Management of Bespoke Tranches | p. 405 |
Summary | p. 406 |
Copula Skew Models | p. 409 |
Introduction | p. 409 |
The Challenge of Fitting the Skew | p. 409 |
Calibration | p. 411 |
Random Recovery | p. 412 |
The Student-t Copula | p. 413 |
The Double-t Copula | p. 415 |
The Composite Basket Model | p. 418 |
The Marshall-Olkin Copula | p. 420 |
The Mixing Copula | p. 421 |
The Random Factor Loading Model | p. 423 |
The Implied Copula | p. 427 |
Copula Comparison | p. 429 |
Pricing Bespokes | p. 431 |
Summary | p. 431 |
Advanced Multi-name Credit Derivatives | p. 433 |
Introduction | p. 433 |
Credit CPPI | p. 433 |
Constant Proportion Debt Obligations | p. 436 |
The CDO-squared | p. 441 |
Tranchelets | p. 448 |
Forward Starting Tranches | p. 449 |
Options on Tranches | p. 449 |
Leveraged Super Senior | p. 450 |
Summary | p. 451 |
Dynamic Bottom-up Correlation Models | p. 453 |
Introduction | p. 453 |
A Survey of Dynamic Models | p. 455 |
The Intensity Gamma Model | p. 458 |
The Affine Jump Diffusion Model | p. 466 |
Summary | p. 470 |
Technical Appendix | p. 470 |
Dynamic Top-down Correlation Models | p. 471 |
Introduction | p. 471 |
The Markov Chain Approach | p. 472 |
Markov Chain: Initial Generator | p. 474 |
Markov Chain: Stochastic Generator | p. 479 |
Summary | p. 483 |
Useful Formulae | p. 485 |
Bibliography | p. 487 |
Index | p. 491 |
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