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**An introduction to credit risk modeling.**
*(English)*
Zbl 1066.91055

Chapman & Hall/CRC Financial Mathematics Series. Boca Raton, FL: Chapman & Hall/CRC (ISBN 1-58488-326-X/hbk; 978-1-4200-5736-2/ebook). 297 p. (2003).

Among the many forms of financial risks the credit risk has attracted more and more attention in recent years. Thus a text on this field has long been overdue. This is an introductory text with the aim to survey the basic methods and points of view on this matter. For detailed information one will thus have to rely on the literature. It is not a text on the mathematical theories of credit risk aimed at students or mathematician, but its goal is rather to give the practitioners, i.e. portfolios analysts in banks and insurance companies the necessary background in this domain. Thus theorems are largely absent and are replaced by explanations and descriptions. For a more mathematically inclined survey see the article by T. R. Bielecki et al in [Lecture Notes Math. 1856, 27–156 (2004; Zbl 1134.91023)]. As an introductory survey it does an admirable job.

In this book risk is mainly understood as risk of default. Unlike insurance risk the data base for credit risk is rather scarce and most often not even well defined. Thus the actual computation of credit risk is based on models with many simplifying assumptions and approximations. A further distinction from insurance mathematics in the correlation between different risks in a portfolio. In fact this is the major challenge from the data point of view, but also from the modeling side.

After some introductory and explanatory material in chapter one, this problem is addressed the following chapter. This section surveys the various models currently employed and presents means to model correlation, notably factor- or sector models or the use of copulas. In particular this section outlines the models which are discussed in the following sections. Thus Merton’s asset value model is presented in section 3. This is the most mathematical section, unencummered by correlations. The Credit Risk model, discussed in the following section, is based on Poisson – default rates with parameters derived from sectors. A key method in analysing the default distributions are probability generating functions. Risk measures, value at risk and expected shorfall are analyzed in section 5.

In intensity models the default rate is modeled as in survival analysis and it can be extracted from historical data. In this case credit migration is a major tool. Other forms could be based on Merton’s model. In chapter 7 various forms of credit derivatives and their use in protection against credit risk are discussed.

In the last chapter collateralized debt obligations as an important class of asset backed securities are introduced. From a mathematical and modeling point of view this section has the least to offer. Thus it is largely a summary and listing of possible forms and set ups.

Summing up, this book is an important guide into the field of credit risk models. Mainly for the practitioner and less for the academician. Its introductory form, however, will make it necessary ever so often to rely on the literature. It is well written, fairly easy to follow. A listing of abreviations used in this book would also be an improvement. Comparing the list of references of the above mentioned paper with this book shows an intersection of about forty titles with an equal amount missing.

A great disadvantage in this book is its lack of criticism. Difficulties in defining, obtaining and using data are glanced over. Take for example, volatility, correlations or factors, which have been discussed extensively in the literature. Thus for practitioners a listing of advantages and disadvantages and a comparison of the various models would be welcome. Finally each chapter should be preceded by a short summary as in chapter 8.

In this book risk is mainly understood as risk of default. Unlike insurance risk the data base for credit risk is rather scarce and most often not even well defined. Thus the actual computation of credit risk is based on models with many simplifying assumptions and approximations. A further distinction from insurance mathematics in the correlation between different risks in a portfolio. In fact this is the major challenge from the data point of view, but also from the modeling side.

After some introductory and explanatory material in chapter one, this problem is addressed the following chapter. This section surveys the various models currently employed and presents means to model correlation, notably factor- or sector models or the use of copulas. In particular this section outlines the models which are discussed in the following sections. Thus Merton’s asset value model is presented in section 3. This is the most mathematical section, unencummered by correlations. The Credit Risk model, discussed in the following section, is based on Poisson – default rates with parameters derived from sectors. A key method in analysing the default distributions are probability generating functions. Risk measures, value at risk and expected shorfall are analyzed in section 5.

In intensity models the default rate is modeled as in survival analysis and it can be extracted from historical data. In this case credit migration is a major tool. Other forms could be based on Merton’s model. In chapter 7 various forms of credit derivatives and their use in protection against credit risk are discussed.

In the last chapter collateralized debt obligations as an important class of asset backed securities are introduced. From a mathematical and modeling point of view this section has the least to offer. Thus it is largely a summary and listing of possible forms and set ups.

Summing up, this book is an important guide into the field of credit risk models. Mainly for the practitioner and less for the academician. Its introductory form, however, will make it necessary ever so often to rely on the literature. It is well written, fairly easy to follow. A listing of abreviations used in this book would also be an improvement. Comparing the list of references of the above mentioned paper with this book shows an intersection of about forty titles with an equal amount missing.

A great disadvantage in this book is its lack of criticism. Difficulties in defining, obtaining and using data are glanced over. Take for example, volatility, correlations or factors, which have been discussed extensively in the literature. Thus for practitioners a listing of advantages and disadvantages and a comparison of the various models would be welcome. Finally each chapter should be preceded by a short summary as in chapter 8.

Reviewer: Horst Behncke (Osnabrück)

### MSC:

91-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance |

91G40 | Credit risk |