Book Review: An Introduction to Credit Risk Modeling

Greg M. Gupton

Abstract

An Introduction to Credit Risk Modeling by Christian Bluhm, Ludger Overbeck and Christoph Wagner, Chapman & Hall/CRC, 2002. 297pp. Hardcover, US$75.00. ISBN: 1-58488-326-X.

An Introduction to Credit Risk Modeling débuted two years ago and it is a safe bet that it will be around for at least another two. The book continues in its popularity for three reasons: it is very readable; it squarely hits the "sweet spot" of formulae-to-prose that is just right; and it is eminently practical. The authors each have experience in the internal risk management functions of large commercial banks. Their backgrounds underscore the most likely buyers of this book: (1) anyone working at a commercial bank or on a buyside credit portfolio; (2) anyone required to deal with or understand vendor credit-VAR models; or (3) anyone new to the details of credit risk modeling who would like to start understanding the math in a gentle way.

The opening chapter sets the tone that this is a book written by skilled practitioners rather than rarified scholars. The reader is immediately shown two handy tricks of the trade that one could likely use many times over. There is also a nice highlighting of techniques that constitute "best practice" as opposed to merely common practice. One caution that the authors themselves underscore in the closing two pages of Chapter 1 is that the book cannot address Basel II since the regulations were too much in flux at the time of writing. These, plus two more Basel-related pages in Chapter 8, total only four pages that have become obsolete since the book's writing. 

Chapter 2 discusses in some detail the methodologies behind the major vended credit-VAR models in approximate proportion to their "market share". These include the MKMV models of EDF and Portfolio- Manager, CreditMetrics, CreditRisk+, CreditPortfolioView, and intensity models. For someone who has to deal with these models as part of their job, this chapter alone is a godsend as it details much of the practical workings and specifics. I personally found paragraph 2.6.1 interesting because it showed me how I could model different copulas (eg, with t-distributed marginals) in an Excel spreadsheet.

The next two chapters give more depth to the two prevailing "camps" of credit VAR modeling approaches. These are the structural frameworks of MKMV and CreditMetrics (Chapter 3) and the insurance-type approach exemplified by CreditRisk+ (Chapter 4). After linking asset-value models to the academic literature, Chapter 3 takes the reader step-by-step through a quick review of option pricing, the mechanics of geometric Brownian motion and the extensions of the Merton "classical" model. The reader is provided with a full framework that will enable him or her to understand the relationships, assumptions and theoretical foundations of the so-called "structural" frameworks. Chapter 4 gives detail to, specifically, the CreditRisk+ framework. After giving a brief overview (which rather repeats a section in Chapter 2), the authors then step through how to build up the specification of obligors, individual sectors, default distributions and compound sectors. I found this very straightforward description to be more readable than the original CreditRisk+ technical document and recommend it to anyone who works with- or whose job is affected by - CreditRisk+.

Chapter 5 is a brief 17-page comment to the effect that value-at-risk is only one possible choice of risk measure. Indeed, for very logical reasons that are known as coherency, VAR may be a poor choice. While I suppose it is good for the reader to be aware of this debate, the seemingly alternative measure, expected shortfall, has its own issues and is more computationally expensive. Overall, I feel this chapter does not add to the goals of the book and I would have advocated leaving it out entirely.

Chapter 6 discusses default term structure modeling. After laying out the nomenclature and notation common to most hazard rate models, the authors give a nice discussion of the difference between risk-neutral and physical default probabilities. The distinction is important because risk-neutral figures are needed for pricing a security. Then, since many models are parameterized with rating agency default data, the authors detail concepts such as default cohorts, transition matrices and Q-generator matrices. Some of their suggestions on how to coerce matrices to be "better behaved" are a bit ad hoc and I would commend a diligent reader to papers such as "Non-parametric analysis of rating transition and default data" by Fledelius, Lando and Nielson (2004) in the Journal of Investment Management, vol. 2(2), pp. 71-85.

The final two chapters embark on necessarily brief surveys of topics that have become enormously wide in the past few years: credit derivatives and credit default swaps. A full treatment of these is better found in other books that are entirely given over to these specialized areas. In their book the authors do a nice job of introducing the topics and relating the specialized models used in these areas to the more general modeling frameworks that are the bread and butter of credit-VAR frameworks.

Chapter 7 presents a nice itemization of the most common credit derivative structures: total return swaps, credit default swaps, baskets, credit spread products, and creditlinked notes. The authors highlight some of the pivotal modeling assumptions, such as correlation estimation. They also touch on the added complexities of counterparty risk.

Chapter 8 is a whirlwind taxonomy of the plethora of CDO structures, with a handy family-tree chart. It is an interesting historical fact that the rating agencies were the leaders in developing models of CDOs, and their legacy, such as the binomial expansion technique (BTE) and the Moody's diversity score, while quaint, are still broadly influential. The authors discuss both, but the original papers are available on www.Moodys.com. 

There is some unevenness in the fit and finish of the book that I might blame on the publisher. For example, I have never before seen formulae continue across on to the next page. This occurs more than once and involves equations that are only two or three lines long. Another criticism is that the notation is sometimes clumsy. For example, in discussing basket credit derivatives, notations for the kthto- default include the "skth" spread and the "F(f:n)kth=i ... probability distribution of the kth order statistic of the default times...".

It is not the purpose of this book to prove that the modeling frameworks presented are good at explaining the empirical evidence, nor to declare any one framework superior to all others, nor even to advocate that one framework should be used by all diligent institutions. Anyone with such agendas is missing the point. The book succeeds wonderfully at its goal, which is to provide the reader with a deeper understanding of the currently available credit risk modeling frameworks.

Mr Gupton is the lead author of CreditMetrics and recently has been leading the loss given default research efforts of MKMV with LossCalc. In his spare time he operates the DefaultRisk.com website.