An Introduction to
Credit Risk Modeling

This is an outstanding book on the default models that are used internally by financial institutions for tasks such as:

economic capital calculations;

pricing credit derivatives, CDOs and other credit sensitive instruments;

calculating utilization of credit risk limits;

marking-to-model illiquid or non-traded debt.

   
 

It is a testament to the available models that they are useful for such disparate purposes. This practical book delves into the mathematics, the assumptions, and the approximations that practitioners apply to make these models work. Unlike most books on credit risk modeling, which tend to focus on either pricing or risk management applications, Bluhm et al cover both well.

The book's focus is on structural default models (the Merton model) and extensions of those models that can be applied to portfolio credit risk. Intensity (reduced form) models are also discussed, but not in as much depth. Early chapters focus on credit risk modeling. The emphasis is on portfolio credit risk and ways of integrating asset value models with some sort of correlation structure for this purpose. Factor and sector correlation models are detailed, as is the use of copulas. Prior knowledge of copulas, as covered by Nelsen (1999), will be helpful. Later chapters turn to financial engineering applications of credit models. These include elementary discussions of modeling credit derivatives and collateralized debt obligations (CDOs).

Two chapters are dedicated to asset value models and the CreditRisk+ model for portfolio credit risk management. Another considers modeling issues related to capital calculations.

The book has two shortcomings. First, its treatment of intensity models lacks depth. For an excellent treatment of those models, see Duffie and Singleton (2003). Second, it does not do a good job of orienting the reader to the subject overall. While modeling techniques are covered well, it is difficult for readers to figure out how each fits into a bigger picture. This is a modest problem. Given enough effort, readers will find there way. However, if you are new to the subject, I encourage you to first read a more elementary book. Either Saunders and Allen (2002) or Crouhy et al. (2001) will be excellent for this purpose.

What really sets this book apart is Chapter 2 on modeling of correlated defaults. It is the best treatment of this material anywhere—recommended reading for anyone interested in 1) modeling portfolio credit risk or 2) pricing CDOs or multiple-obligor credit derivatives.

Contents

1. The Basics of Credit Risk Management

Expected Loss

Unexpected Loss

Regulatory Capital and the Basel Initiative

2. Modeling Correlated Defaults

The Bernoulli Model

The Poisson Model

Bernoulli Versus Poisson Mixture

An Overview of Today's Industry Models

One-Factor/Sector Models

Loss Distributions by Means of Copula Functions

Working Example: Estimation of Asset Correlations

3. Asset Value Models

Introduction and a Small Guide to the Literature

A Few Words about Calls and Puts

Merton's Asset Value Model

Transforming Equity into Asset Values: A Working Approach

4. The CreditRisk+ Model

The Modeling Framework of CreditRisk+

Construction Step 1: Independent Obligors

Construction Step 2: Sector Model

5. Alternative Risk Measures and Capital Allocation

Coherent Risk Measures and Conditional Shortfall

Contributory Capital

6. Term Structure of Default Probability

Survival Function and Hazard Rate

Risk-neutral vs. Actual Default Probabilities

Term Structure Based on Historical Default Information

Term Structure Based on Market Spreads

7. Credit Derivatives

Total Return Swaps

Credit Default Products

Basket Credit Derivatives

Credit Spread Products

Credit-linked Notes

8. Collateralized Debt Obligations

Introduction to Collateralized Debt Obligations

Different Roles of Banks in the CDO Market

CDOs from the Modeling Point of View

Rating Agency Models: Moody's BET

Conclusion

Some Remarks on the Literature

The book is probably most useful for readers interested in risk management applications of credit risk models—for this purpose, its discussions are cutting-edge. For readers interested in credit derivative or CDO pricing, the treatment of structural default models is excellent, but discussions of implementation are disappointing. For such readers, the book is a nice complement to Duffie and Singleton (2003), which emphasizes intensity models. It is also an excellent book to read before proceeding to the authoritative but more advanced Schönbucher's (2003).

 

 

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