The quantification of risk is playing an increasingly important role in finance with regulatory regimes such as Solvency II requiring more detail of financial companies’ risks. This book's aims are to bring the work of the authors’ academic work on Operational Risk to a more general audience and to practitioners in particular. They do this by considering a number of statistical distributions generally thought appropriate for modelling Operational Risk and comparing the results with real life data, adding in more and more complications as the book progresses. The last portion of the book contains a comprehensive set of computer programs in SAS and R illustrating the concepts introduced.
The first chapter introduces the concept of operational risk by comparing the risks in a non-financial company, where the breakdown of an important piece of machinery may cause significant loss. It also points out where the comparison breaks down, for example it may not immediately be apparent that there has been a breakdown in processes in a financial company. It then considers other potential issues such as sparse data before giving more information on the Basel regulations as the Solvency II details were not known at the time of writing. The methods used to compare the different statistical distributions are also considered, particularly Value at Risk and Tail Value at Risk.
The first distributions to be introduced are parametric models such as the Logistic, Gamma, Weibull and Lognormal which should be recognisable to most actuaries. The authors introduce the Generalized Champernowne distribution which is similar to a Pareto in the tail and a Lognormal near 0 as an alternative. The authors then use five companies’ data against each distribution to compare the Value at risk against an industry data set.
The third chapter introduces semi parametric models. The authors think this is more suitable as there is more flexibility allowing for different shapes of distribution in the tails compared with smaller losses. The main approach focuses on the semi-parametric approach to kernel smoothing and allows for setting bandwidths and considers boundary correction. It then applies these principles to the Generalized Champernoewne distribution before a comparison of how the individual companies and industry data fit with this revision.
As the data events for operational risks are generally sparse a further improvement the authors consider is combining the company data with industry wide data such that an appropriate level of weighting is given to the data sources. When the results are compared they are for a particular company which compares the results using just the company's data, using only the internal data and a variety of methods of mixing the two data sets.
Chapter 5 investigates the effects of underreporting, the effect that not all operational risk claims will be reported. The authors deal with this by comparing expert opinions with publicly available data allowing an underreporting function to be calculated which can be used as an estimator of the underlying true loss distribution. This was then modelled using cubic splines. The causes of underlying claim were separated out for this analysis, with the most underreported source being the Execution, Delivery and Process Management category. The effects of these were then applied to the semi parametric models with fairly similar outcomes being available for each model choice. This was in contrast to the model choice being crucial where only parametric models were being used.
The next chapter combines the elements underreporting and using external data. This is done by assuming that all losses under a particular threshold are not reported and then develops more models taking account of the external data. The loss distributions for a variety of the models developed through the book are then presented and compared and contrasted.
The last chapter and largest, and perhaps the most useful to practitioners, is the example code in R and SAS. These are presented with notes and output so that anyone investigating the code can better understand the output. If data is required to replicate the computer code then this is available from the authors.
One of the best things about the book was a brief summary of the further reading they recommended, making it possible to see which papers would be particularly relevant if further information was needed. Additionally there was sufficient working where any more unusual mathematical results were required.
Overall the book presents a very useful addition to the literature on Operational Financial Risk and I would recommend it to practitioners.
