Bayesian Inference, Monte Carlo Sampling and Operational Risk.

 Peters G.W. and Sisson S.A. (2006) “Bayesian Inference, Monte Carlo Sampling and Operational Risk". Journal of Operational Risk, 1(3).

24 Pages Posted: 5 Jun 2017

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Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Scott Sisson

University of New South Wales (UNSW) - School of Mathematics and Statistics

Date Written: 2006

Abstract

Operational risk is an important quantitative topic as a result of the Basel II regulatory requirements. Operational risk models need to incorporate internal and external loss data observations in combination with expert opinion surveyed from business specialists. Following the Loss Distributional Approach, this article considers three aspects of the Bayesian approach to the modelling of operational risk. Firstly we provide an overview of the Bayesian approach to operational risk, before expanding on the current literature through consideration of general families of non-conjugate severity distributions, g-and-h and GB2 distributions. Bayesian model selection is presented as an alternative to popular frequentist tests, such as Kolmogorov-Smirnov or Anderson-Darling. We present a number of examples and develop techniques for parameter estimation for general severity and frequency distribution models from a Bayesian perspective. Finally we introduce and evaluate recently developed stochastic sampling techniques and highlight their application to operational risk through the models developed.

Keywords: Approximate Bayesian Computation; Basel II Advanced Measurement Approach; Bayesian Inference; Compound Processes; Loss Distributional Approach; Markov Chain Monte Carlo; Operational Risk

Suggested Citation

Peters, Gareth and Sisson, Scott, Bayesian Inference, Monte Carlo Sampling and Operational Risk. (2006).  Peters G.W. and Sisson S.A. (2006) “Bayesian Inference, Monte Carlo Sampling and Operational Risk". Journal of Operational Risk, 1(3). , Available at SSRN: https://ssrn.com/abstract=2980407 or http://dx.doi.org/10.2139/ssrn.2980407

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Scott Sisson

University of New South Wales (UNSW) - School of Mathematics and Statistics ( email )

Sydney, 2052
Australia

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