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Modelling Single-name and Multi-name Credit Derivatives
O’Kane, Dominique
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Últimas novedades
management
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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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Acknowledgements
About the Author
Introduction
Notation
1 The Credit Derivatives Market
1.1 Introduction
1.2 Credit Derivatives Market Size
1.3 Products
1.4 Market Participants
2 Building the Libor Discount Curve
2.1 Introduction
2.2 The Libor Index
2.3 Money Market Deposits
2.4 Forward Rate Agreements
2.5 Interest Rate Futures
2.6 Interest Rate Swaps
2.7 Bootstrapping the Libor Curve
2.8 Summary
2.9 Technical Appendix
PART I SINGLE-NAME CREDIT DERIVATIVES
3 Single-name Credit Modelling
3.1 Introduction
3.2 Observing Default
3.3 Risk-neutral Pricing Framework
3.4 Structural Models of Default
3.5 Reduced Form Models
3.6 The Hazard Rate Model
3.7 Modelling Default as a Cox Process
3.8 A Gaussian Short Rate and Hazard Rate Model
3.9 Independence and Deterministic Hazard Rates
3.10 The Credit Triangle
3.11 The Credit Risk Premium
3.12 Summary
3.13 Technical Appendix
4 Bonds and Asset Swaps
4.1 Introduction
4.2 Fixed Rate Bonds
4.3 Floating Rate Notes
4.4 The Asset Swap
4.5 The Market Asset Swap
4.6 Summary
5 The Credit Default Swap
5.1 Introduction
5.2 The Mechanics of the CDS Contract
5.3 Mechanics of the Premium Leg
5.4 Mechanics of the Protection Leg
5.5 Bonds and the CDS Spread
5.6 The CDS–Cash basis
5.7 Loan CDS
5.8 Summary
6 A Valuation Model for Credit Default Swaps
6.1 Introduction
6.2 Unwinding a CDS Contract
6.3 Requirements of a CDS Pricing Model
6.4 Modelling a CDS Contract
6.5 Valuing the Premium Leg
6.6 Valuing the Protection Leg
6.7 Upfront Credit Default Swaps
6.8 Digital Default Swaps
6.9 Loan CDS
6.10 Summary
7 Calibrating the CDS Survival Curve
7.1 Introduction
7.2 Desirable Curve Properties
7.3 The Bootstrap
7.4 Interpolation Quantities
7.5 Bootstrapping Algorithm
7.6 Behaviour of the Interpolation Scheme
7.7 Detecting Arbitrage in the Curve
7.8 Example CDS Valuation
7.9 Summary
8 CDS Risk Management
8.1 Introduction
8.2 Market Risks of a CDS Position
8.3 Analytical CDS Sensitivities
8.4 Full Hedging of a CDS Contract
8.5 Hedging the CDS Spread Curve Risk
8.6 Hedging the Libor Curve Risk
8.7 Portfolio Level Hedging
8.8 Counterparty Risk
8.9 Summary
9 Forwards, Swaptions and CMDS
9.1 Introduction
9.2 Forward Starting CDS
9.3 The Default Swaption
9.4 Constant Maturity Default Swaps
9.5 Summary
PART II MULTI-NAME CREDIT DERIVATIVES
10 CDS Portfolio Indices
10.1 Introduction
10.2 Mechanics of the Standard Indices
10.3 CDS Portfolio Index Valuation
10.4 The Index Curve
10.5 Calculating the Intrinsic Spread of an Index
10.6 The Portfolio Swap Adjustment
10.7 Asset-backed and Loan CDS Indices
10.8 Summary
11 Options on CDS Portfolio Indices
11.1 Introduction
11.2 Mechanics
11.3 Valuation of an Index Option
11.4 An Arbitrage-free Pricing Model
11.5 Examples of Pricing
11.6 Risk Management
11.7 Black’s Model Revisited
11.8 Summary
12 An Introduction to Correlation Products
12.1 Introduction
12.2 Default Baskets
12.3 Leveraging the Spread Premia
12.4 Collateralised Debt Obligations
12.5 The Single-tranche Synthetic CDO
12.6 CDOs and Correlation
12.7 The Tranche Survival Curve
12.8 The Standard Index Tranches
12.9 Summary
13 The Gaussian Latent Variable Model
13.1 Introduction
13.2 The Model
13.3 The Multi-name Latent Variable Model
13.4 Conditional Independence
13.5 Simulating Multi-name Default
13.6 Default Induced Spread Dynamics
13.7 Calibrating the Correlation
13.8 Summary
14 Modelling Default Times using Copulas
14.1 Introduction
14.2 Definition and Properties of a Copula
14.3 Measuring Dependence
14.4 Rank Correlation
14.5 Tail Dependence
14.6 Some Important Copulae
14.7 Pricing Credit Derivatives from Default Times
14.8 Standard Error of the Breakeven Spread
14.9 Conclusions
14.10 Technical Appendix
15 Pricing Default Baskets
15.1 Introduction
15.2 Modelling First-to-default Baskets
15.3 Second-to-default and Higher Default Baskets
15.4 Pricing Baskets using Monte Carlo
15.5 Pricing Baskets using a Multi-Factor Model
15.6 Pricing Baskets in the Student-t Copula
15.7 Risk Management of Default Baskets
15.8 Summary
16 Pricing Tranches in the Gaussian Copula Model
16.1 Introduction
16.2 The LHP Model
16.3 Drivers of the Tranche Spread
16.4 Accuracy of the LHP Approximation
16.5 The LHP Model with Tail Dependence
16.6 Conclusion
16.7 Technical Appendix
17 Risk Management of Synthetic Tranches
17.1 Introduction
17.2 Systemic Risks
17.3 The LH+ Model
17.4 Idiosyncratic Risks
17.5 Hedging Tranches
17.6 Conclusion
17.7 Technical Appendix
18 Building the Full Loss Distribution
18.1 Introduction
18.2 Calculating the Tranche Survival Curve
18.3 Building the Conditional Loss Distribution
18.4 Integrating over the Market Factor
18.5 Approximating the Conditional Portfolio Loss Distribution
18.6 A Comparison of Methods
18.7 Perturbing the Loss Distribution
18.8 Summary
19 Implied Correlation
19.1 Introduction
19.2 Implied Correlation
19.3 Compound Correlation
19.4 Disadvantages of Compound Correlation
19.5 No-arbitrage Conditions
19.6 Summary
20 Base Correlation
20.1 Introduction
20.2 Base Correlation
20.3 Building the Base Correlation Curve
20.4 Base Correlation Interpolation
20.5 Interpolating Base Correlation using the ETL
20.6 A Base Correlation Surface
20.7 Risk Management of Index Tranches
20.8 Hedging the Base Correlation Skew
20.9 Base Correlation for Bespoke Tranches
20.10 Risk Management of Bespoke Tranches
20.11 Conclusions
21 Copula Skew Models
21.1 Introduction
21.2 The challenge of Fitting the Skew
21.3 Calibration
21.4 Random Recovery
21.5 The Student-t Copula
21.6 The Double-t Copula
21.7 The Composite Basket Model
21.8 Marshall–Olkin Copula
21.9 Mixing Copula Model
21.10 The Random Factor Loading Model
21.11 The Implied Copula
21.12 Copula Comparison
21.13 Pricing Bespokes
21.14 Summary
22 Advanced Multi-name Credit Derivatives
22.1 Introduction
22.2 Credit CPPI
22.3 Constant Proportion Debt Obligations
22.4 The CDO-squared
22.5 Tranchelets
22.6 Forward Starting Tranches
22.7 Options on Tranches
22.8 Leveraged Super Senior
22.9 Conclusions
23 Dynamic Bottom-up Correlation Models
23.1 Introduction
23.2 A Survey of Dynamic Models
23.3 The Intensity Gamma Model
23.4 The Affine Jump Diffusion Model
23.5 Conclusions
23.6 Technical Appendix
24 Dynamic Top-down Correlation Models
24.1 Introduction
24.2 The Markov Chain Approach
24.3 Markov Chain: Initial Generator
24.4 Markov Chain: Stochastic Generator
24.5 Conclusions
Appendix A Useful Formulae
Bibliography
Index
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