Modelling Single-name and Multi-name Credit Derivatives

Abstract

Contents 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

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 138 citations exist upstream.