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Modelling operational risk using Bayesian inference. (English) Zbl 1213.91011

Berlin: Springer (ISBN 978-3-642-15922-0/hbk). xvii, 302 p. (2011).
The management of operational risk in the banking industry has undergone significant changes over the last decade due to the substantial changes in the operational environment. In response to these changes, the Basel Committee on Banking Supervision has developed a new regulatory framework for capital measurement and standards for the banking sector. This has formally defined operational risk and introduced corresponding capital requirements. To satisfy these requirements, many banks are undertaking quantitative modelling of operational risk under the so-called Basel II advanced measurement approaches (AMA), and especially the loss distribution approach (LDA), a popular method under the AMA, which is based on statistical quantification of the frequency and severity of operational risk losses. This book is devoted to quantitative issues in LDA. In particular, the use of Bayesian inference is its main focus. Though it is very new in this area, the Bayesian approach is well suited for modelling operational risk, as it allows for a consistent and convenient statistical framework for quantifying the uncertainties involved. It also allows for the combination of expert opinion with historical internal and external data in estimation procedures, which are critical, especially for operational risks that have small datasets.
Organised in seven chapters, the book starts from an introduction to operational risk and the Basel II approaches for its quantification. Then, in Chapters 2 and 3, respectively, it presents and discusses a basic model for LDA, and the evaluation of compound loss distributions necessary for the estimation of capital under the LDA. Chapter 4 presents examples of the Bayesian inference and closely related credibility theory methods for quantifying operational risk, while Chapter 5 addresses the data truncation problem. Chapter 6 discusses extreme value theory, which allows analysts to rationally extrapolate to losses beyond those historically observed, and to estimate their probability, as well as several parametric distributions, which have been proposed to model the tail distribution of operational risk losses. Finally, Chapter 7 considers how to model dependence between operational risks. It presents different approaches and issues, which are debated in the literature, and discusses conceptual problems with the dominance of heavy-tailed risks in the capital charge and possible failed diversification. The book provides also a comprehensive list of references to guide more advanced readers through the vast literature and take them to the frontier of practically relevant research. Due to confidentiality issues, the book does not include examples of real operational risk data. Instead, illustrative examples with realistic parameter values are used to demonstrate the notions presented within it.
The book is aimed at practitioners in risk management, academic researchers in financial mathematics, banking industry regulators and advanced graduate students in the area.

MSC:

91-02 Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62F15 Bayesian inference

Software:

AMCMC; STABLE; UNCMND
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