Credit

Introduction

PART I - CREDIT RISK MANAGEMENT

1 - Overview of Credit Risk

1.1 Components of Credit Risk

1.2 Factors Determining the Credit Risk of a Portfolio

1.3 Traditional Approaches to Managing Credit Risk

1.4 Market Risk versus Credit Risk

1.5 Historical Data

1.6 Example of Default Loss Distribution

1.7 Credit Risk Models

1.8 Conclusion

2 - Exposure Measurement

2.1 Introduction

2.2 Exposure Simulation

2.3 Typical Exposures

2.4 Conclusion

3 - A Framework for Credit Risk Management

3.1 Credit Loss Distribution and Unexpected Loss

3.2 Generating the Loss Distribution

3.3 Example - One Period Model

3.4 Multiple Period Model

3.5 Loan Equivalents

3.6 Conclusion

Appendix

Derivation of the Formulas for Loan Equivalent Exposures

4 - Extensions of the General Framework

4.1 Analytical Approximations to the Loss Distribution

4.2 Monte Carlo Acceleration Techniques

4.3 Extreme Value Theory

4.4 Marginal Risk

4.5 Portfolio Optimisation

4.6 Conclusion

PART II - PRICING AND HEDGING OF CREDIT RISK

5 - Credit Derivatives

5.1 Default Swaps, Asset Swaps and Risky Bonds

5.2 Worst-of and Baskets

5.3 Other Credit Contingent Contracts

5.4 Other Products and Exotics

5.5 Conclusion

6 - Pricing Counterparty Risk in Interest Rate Derivatives

6.1 Introduction

6.2 Overview

6.3 Expected Loss versus Economic Capital

6.4 Portfolio Effect

6.5 Market Variables

6.6 Interest Rate Swaps

6.7 Cross Currency Swaps

6.8 Caps and Floors

6.9 Swaptions

6.10 Portfolio Pricing

6.11 Extensions of the Model

6.12 Hedging

6.13 Conclusion

Appendices

Appendix A - Derivation of the Formula for the Expected Loss on an Interest Rate Swap

Appendix B - The Formula for the Expected Loss on an Interest Rate Cap or Floor

Appendix C - Derivation of the Formula for the Expected Loss on an Interest Rate Swaption (Hull and White Interest Rate Model)

Appendix D - Derivation of the Formula for the Expected Loss on a Cancellable Interest Rate Swap

Appendix E - Market Parameters used for the Computations

7 - Credit Risk in Convertible Bonds

7.1 Introduction

7.2 Basic Features of Convertibles

7.3 General Pricing Conditions

7.4 Interest Rate Model

7.5 Firm Value Model

7.6 Credit Spread Model

7.7 “Link“ of the two Models

7.8 Hedging of Credit Risk

7.9 Conclusion

Appendices

Appendix A - Firm Value Model - Analytic Pricing Formulae

Appendix B - Derivation of Formulae for Trinomial Tree with Default Branch

Appendix C - Effect of Sub-optimal Call Policy

Appendix D - Incorporation of “Smile“ in the Firm Value Model

8 - Market Imperfections

8.1 Liquidity Risk

8.2 Discrete Hedging

8.3 Asymmetric Information

8.4 Conclusion

Appendix

1. Credit Swap Valuation Darrel Duffie

2. Practical use of Credit Risk Models in Loan Portfolio and Counterparty Exposure Management Robert A. Jarrow and Donald R. van Deventer

3. An Empirical Analysis of Corporate Rating Migration, Default and Recovery Sean C. Keenan, Lea V. Carty and David T. Hamilton

4. Modelling Credit Migration Bill Demchak

5. Haircuts for Hedge Funds Ray Meadows

6. Generalising with HJM Dmitry Pugachevsky

Glossary

Index