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Modelling Single-name and Multi-name Credit Derivatives

Modelling Single-name and Multi-name Credit Derivatives

  • Author:
  • Publisher: John Wiley & Sons
  • ISBN: 9780470519288
  • Published In: July 2008
  • Format: Hardback , 514 pages
  • Jurisdiction: International ? Disclaimer:
    Countri(es) stated herein are used as reference only
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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.

     

  • 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

     

  • 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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