Credit
The Complete Guide to Pricing, Hedging and Risk Management

Hold onto your seats! Arvanitis and Gregory have written a tour de force of credit risk modeling. They discuss both the modeling of portfolio credit risk and the pricing of credit sensitive instruments:

OTC derivatives,

credit derivatives,

convertible bonds,

collateralized debt obligations (CDOs), etc.

While other books offer a survey of techniques, Arvanitis and Gregory are more prescriptive, describing in a soup-to-nuts manner how to implement the models they recommend. This is nice because it enables them to delve deeply into practical details other books don't have time for. For example, they describe how to use the Edgeworth expansion to construct a control variate for a portfolio's value—and then use the control variate to implement variance reduction in a Monte Carlo analysis of portfolio credit risk. The discussion is sophisticated, mathematically elegant, and very practical. Even if you use different models, the technique will be largely transferable.

 

Primarily, the authors use intensity (reduced form) models for both portfolio credit risk and financial engineering. However, they explain how structural models (the Merton model) can be useful for certain pricing applications.

Mathematically sophisticated readers will love the book. The mathematics is presented with a light, almost conversational touch. Don't be fooled! There is a lot going on here. Readers with weaker math backgrounds may want to brush up on some topics before progressing to Arvanitis and Gregory. See in particular my book, Holton (2003), on value-at-risk. It covers in depth much of the mathematics that Arvanitis and Gregory assume—topics like the inversion theorem of probability, moment generating functions, and variance reduction for Monte Carlo analysis. Read also Duffie and Singleton (2003) or the more advanced Schönbucher's (2003). Either will give you a solid background on intensity models as well as a number of the modeling techniques Arvanitis and Gregory elaborate on.

Discussions of pricing credit derivatives are light on theory but heavy on practice. Pricing strategies are detailed for a variety of instruments, culminating with one of the best examples I have seen for pricing a simple CDO. In this regard, the book makes a nice complement to the more theoretical Schönbucher's (2003)

Chapters on potential credit exposure for OTC derivatives and on pricing convertible bonds are surprisingly sophisticated—more so than the somewhat more accessible discussions of the same topics in Duffie and Singleton (2003).

The only shortcoming I see of the book is its discussion of default correlation modeling, which does not reflect recent advances. See Bluhm et al (2002) or Schönbucher's (2003) instead.

 

Contents

PART I - CREDIT RISK MANAGEMENT

1. Overview of Credit Risk

Components of Credit Risk

Factors Determining the Credit Risk of a Portfolio

Traditional Approaches to Managing Credit Risk

Market Risk versus Credit Risk

Historical Data

Example of Default Loss Distribution

Credit Risk Models

2. Exposure Measurement

Exposure Simulation

Typical Exposures

3. A Framework for Credit Risk Management

Credit Loss Distribution and Unexpected Loss

Generating the Loss Distribution

Example - One Period Model

Multiple Period Model

Loan Equivalents

Appendix  - Derivation of the Formulas for Loan Equivalent Exposures

4. Extensions of the General Framework

Analytical Approximations to the Loss Distribution

Monte Carlo Acceleration Techniques

Extreme Value Theory

Marginal Risk

Portfolio Optimization

PART II - PRICING AND HEDGING OF CREDIT RISK

5 - Credit Derivatives

Default Swaps, Asset Swaps and Risky Bonds

Worst-of and Baskets

Other Credit Contingent Contracts

Other Products and Exotics

6. Pricing Counterparty Risk in Interest Rate Derivatives

Overview

Expected Loss versus Economic Capital

Portfolio Effect

Market Variables

Interest Rate Swaps

Cross Currency Swaps

Caps and Floors

Swaptions

Portfolio Pricing

Extensions of the Model

Hedging

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

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

Appendix E - Market Parameters used for the Computations

7. Credit Risk in Convertible Bonds

Basic Features of Convertibles

General Pricing Conditions

Interest Rate Model

Firm Value Model

Credit Spread Model

"Link" of the two Models

Hedging of Credit Risk

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

Liquidity Risk

Discrete Hedging

Asymmetric Information

Appendix

1. Credit Swap Valuation Darrel Duffie

2. Practical use of Credit Risk Models in Loan Portfolio and Counterparty Exposure Management

3. An Empirical Analysis of Corporate Rating Migration, Default and Recovery

4. Modelling Credit Migration

5. Haircuts for Hedge Funds

6. Generalizing with HJM

Overall, I can't recommend this book highly enough. For sophisticated readers interested in credit risk modeling, it is a gem!
 

 

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