Modelling Single-Name and Multi-Name Credit Derivatives

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2008-08-04
  • Publisher: WILEY
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The credit derivatives market has grown significantly and rapidly over the past 8 years. However, it is only in the last 4 years that we have seen the advent of the CDS index portfolios such as CDX and iTraxx and their rapid domination of the market. These have revolutionised the credit derivatives market, increasing liquidity and significantly broadening the user base. On top of this, we also have the arrival of CDO tranches linked to these portfolios which has resulted in large and liquid market in default correlation, something that was almost unimaginable 4 years ago. This has created significant challenges for credit modellers as it has essentially rendered earlier correlation models unusable. The search for new approaches has produced a set of new and competing models, all vying to become the new standard. Other products have arrived which have also presented new challenges to credit modellers. These include constant maturity default swaps, options on CDS indices, and CDO squareds, to name just a few. This book covers all of the theory of credit in detail and also covers all of the new developments listed above. Most of the current treatments of the credit derivatives markets are authored by academics (Schonbucher, Duffie&Singleton, Hull) and so are strong on the mathematics. They are usually weak on products descriptions, discussions of the risks, realistic examples, development of model intuition and discussions of the practicalities of implementing the model for the pricing and risk management of credit derivatives in a real industrial setting like an investment bank. Other treatments by practitioners (Chaplin, Tavakoli) tend to be out of date and tend not to get highly technical in the mathematical and implementational detail. O'Kane's aim is to fill the gap by with something which is technical, practical and accessible in the sense that the mathematical treatment is more of a physics/engineering style. It should therefore be useful to the practising quant, risk-manager or student seeking information on how these models are selected and used in reality.

Author Biography

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.

Table of Contents

Acknowledgementsp. xiii
About the Authorp. xv
Introductionp. xvii
Notationp. xix
The Credit Derivatives Marketp. 1
Introductionp. 1
Market Growthp. 2
Productsp. 4
Market Participantsp. 6
Summaryp. 7
Building the Libor Discount Curvep. 9
Introductionp. 9
The Libor Indexp. 9
Money Market Depositsp. 10
Forward Rate Agreementsp. 12
Interest Rate Futuresp. 13
Interest Rate Swapsp. 16
Bootstrapping the Libor Curvep. 21
Summaryp. 26
Technical Appendixp. 26
Single-Name Credit Derivativesp. 29
Single-name Credit Modellingp. 31
Introductionp. 31
Observing Defaultp. 32
Risk-neutral Pricing Frameworkp. 35
Structural Models of Defaultp. 38
Reduced Form Modelsp. 42
The Hazard Rate Modelp. 44
Modelling Default as a Cox Processp. 46
A Gaussian Short Rate and Hazard Rate Modelp. 49
Independence and Deterministic Hazard Ratesp. 51
The Credit Trianglep. 54
The Credit Risk Premiump. 55
Summaryp. 57
Technical Appendixp. 57
Bonds and Asset Swapsp. 59
Introductionp. 59
Fixed Rate Bondsp. 60
Floating Rate Notesp. 68
The Asset Swapp. 72
The Market Asset Swapp. 78
Summaryp. 80
The Credit Default Swapp. 81
Introductionp. 81
The Mechanics of the CDS Contractp. 82
Mechanics of the Premium Legp. 84
Mechanics of the Protection Legp. 85
Bonds and the CDS Spreadp. 90
The CDS-Cash basisp. 92
Loan CDSp. 94
Summaryp. 95
A Valuation Model for Credit Default Swapsp. 97
Introductionp. 97
Unwinding a CDS Contractp. 97
Requirements of a CDS Pricing Modelp. 99
Modelling a CDS Contractp. 100
Valuing the Premium Legp. 101
Valuing the Protection Legp. 105
Upfront Credit Default Swapsp. 108
Digital Default Swapsp. 110
Valuing Loan CDSp. 111
Summaryp. 112
Calibrating the CDS Survival Curvep. 113
Introductionp. 113
Desirable Curve Propertiesp. 113
The Bootstrapp. 114
Interpolation Quantitiesp. 115
Bootstrapping Algorithmp. 117
Behaviour of the Interpolation Schemep. 118
Detecting Arbitrage in the Curvep. 121
Example CDS Valuationp. 123
Summaryp. 125
CDS Risk Managementp. 127
Introductionp. 127
Market Risks of a CDS Positionp. 127
Analytical CDS Sensitivitiesp. 128
Full Hedging of a CDS Contractp. 138
Hedging the CDS Spread Curve Riskp. 139
Hedging the Libor Curve Riskp. 145
Portfolio Level Hedgingp. 147
Counterparty Riskp. 148
Summaryp. 149
Forwards, Swaptions and CMDSp. 151
Introductionp. 151
Forward Starting CDSp. 151
The Default Swaptionp. 156
Constant Maturity Default Swapsp. 169
Summaryp. 180
Multi-Name Credit Derivativesp. 181
CDS Portfolio Indicesp. 183
Introductionp. 183
Mechanics of the Standard Indicesp. 184
CDS Portfolio Index Valuationp. 188
The Index Curvep. 190
Calculating the Intrinsic Spread of an Indexp. 192
The Portfolio Swap Adjustmentp. 195
Asset-backed and Loan CDS Indicesp. 200
Summaryp. 201
Options on CDS Portfolio Indicesp. 203
Introductionp. 203
Mechanicsp. 203
Valuation of an Index Optionp. 207
An Arbitrage-free Pricing Modelp. 209
Examples of Pricingp. 213
Risk Managementp. 215
Black's Model Revisitedp. 215
Summaryp. 217
An Introduction to Correlation Productsp. 219
Introductionp. 219
Default Basketsp. 219
Leveraging the Spread Premiap. 227
Collateralised Debt Obligationsp. 230
The Single-tranche Synthetic CDOp. 232
CDOs and Correlationp. 236
The Tranche Survival Curvep. 237
The Standard Index Tranchesp. 240
Summaryp. 240
The Gaussian Latent Variable Modelp. 241
Introductionp. 241
The Modelp. 241
The Multi-name Latent Variable Modelp. 243
Conditional Independencep. 246
Simulating Multi-name Defaultp. 248
Default Induced Spread Dynamicsp. 253
Calibrating the Correlationp. 257
Summaryp. 258
Modelling Default Times using Copulasp. 261
Introductionp. 261
Definition and Properties of a Copulap. 261
Measuring Dependencep. 264
Rank Correlationp. 265
Tail Dependencep. 269
Some Important Copulaep. 270
Pricing Credit Derivatives from Default Timesp. 278
Standard Error of the Breakeven Spreadp. 280
Summaryp. 281
Technical Appendixp. 282
Pricing Default Basketsp. 283
Introductionp. 283
Modelling First-to-default Basketsp. 283
Second-to-default and Higher Default Basketsp. 291
Pricing Baskets using Monte Carlop. 294
Pricing Baskets using a Multi-Factor Modelp. 296
Pricing Baskets in the Student-t Copulap. 298
Risk Management of Default Basketsp. 299
Summaryp. 301
Pricing Tranches in the Gaussian Copula Modelp. 303
Introductionp. 303
The LHP Modelp. 303
Drivers of the Tranche Spreadp. 308
Accuracy of the LHP Approximationp. 312
The LHP Model with Tail Dependencep. 313
Summaryp. 314
Technical Appendixp. 314
Risk Management of Synthetic Tranchesp. 317
Introductionp. 317
Systemic Risksp. 318
The LH+ Modelp. 324
Idiosyncratic Risksp. 328
Hedging Tranchesp. 334
Summaryp. 339
Technical Appendixp. 339
Building the Full Loss Distributionp. 343
Introductionp. 343
Calculating the Tranche Survival Curvep. 343
Building the Conditional Loss Distributionp. 345
Integrating over the Market Factorp. 353
Approximating the Conditional Portfolio Loss Distributionp. 354
A Comparison of Methodsp. 360
Perturbing the Loss Distributionp. 362
Summaryp. 364
Implied Correlationp. 365
Introductionp. 365
Implied Correlationp. 365
Compound Correlationp. 367
Disadvantages of Compound Correlationp. 370
No-arbitrage Conditionsp. 371
Summaryp. 374
Base Correlationp. 375
Introductionp. 375
Base Correlationp. 375
Building the Base Correlation Curvep. 377
Base Correlation Interpolationp. 382
Interpolating Base Correlation using the ETLp. 389
A Base Correlation Surfacep. 393
Risk Management of Index Tranchesp. 394
Hedging the Base Correlation Skewp. 395
Base Correlation for Bespoke Tranchesp. 398
Risk Management of Bespoke Tranchesp. 405
Summaryp. 406
Copula Skew Modelsp. 409
Introductionp. 409
The Challenge of Fitting the Skewp. 409
Calibrationp. 411
Random Recoveryp. 412
The Student-t Copulap. 413
The Double-t Copulap. 415
The Composite Basket Modelp. 418
The Marshall-Olkin Copulap. 420
The Mixing Copulap. 421
The Random Factor Loading Modelp. 423
The Implied Copulap. 427
Copula Comparisonp. 429
Pricing Bespokesp. 431
Summaryp. 431
Advanced Multi-name Credit Derivativesp. 433
Introductionp. 433
Credit CPPIp. 433
Constant Proportion Debt Obligationsp. 436
The CDO-squaredp. 441
Trancheletsp. 448
Forward Starting Tranchesp. 449
Options on Tranchesp. 449
Leveraged Super Seniorp. 450
Summaryp. 451
Dynamic Bottom-up Correlation Modelsp. 453
Introductionp. 453
A Survey of Dynamic Modelsp. 455
The Intensity Gamma Modelp. 458
The Affine Jump Diffusion Modelp. 466
Summaryp. 470
Technical Appendixp. 470
Dynamic Top-down Correlation Modelsp. 471
Introductionp. 471
The Markov Chain Approachp. 472
Markov Chain: Initial Generatorp. 474
Markov Chain: Stochastic Generatorp. 479
Summaryp. 483
Useful Formulaep. 485
Bibliographyp. 487
Indexp. 491
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