An Application of Bayesian Inference on the Modeling and Estimation of Operational Risk Using Banking Loss Data

ABSTRACT

Bayesian inference method has been presented in this paper for the modeling of operational risk. Bank internal and external data are divided into defined loss cells and then fitted into probability distributions. The distribution parameters and their uncertainties are estimated from posterior distributions derived using the Bayesian inference. Loss frequency is fitted into Poisson distributions. While the Poisson parameters, in a similar way, are defined by a posterior distribution developed using Bayesian inference. Bank operation loss typically has some low frequency but high magnitude loss data. These heavy tail low frequency loss data are divided into several buckets where the bucket frequencies are defined by the experts. A probability distribution, as defined by the internal and external data, is used for these data. A Poisson distribution is used for the bucket frequencies. However instead of using any distribution of the Poisson parameters, point estimations are used. Monte Carlo simulation is then carried out to calculate the capital charge of the in- ternal as well as the heavy tail high profile low frequency losses. The output of the Monte Carlo simulation defines the capital requirement that has to be allocated to cover potential operational risk losses for the next year.

Cite this paper

Rahman, K. , Black, D. and McDonald, G. (2014) An Application of Bayesian Inference on the Modeling and Estimation of Operational Risk Using Banking Loss Data.*Applied Mathematics*, **5**, 862-876. doi: 10.4236/am.2014.56082.

Rahman, K. , Black, D. and McDonald, G. (2014) An Application of Bayesian Inference on the Modeling and Estimation of Operational Risk Using Banking Loss Data.

References

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http://dx.doi.org/10.1007/978-3-642-15923-7

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http://dx.doi.org/10.1007/978-3-642-15923-7

[2] King, J.L. (2001) Operational Risk Measurement and Modeling. Wiley.

[3] Cruz, M.G. (2002) Modeling, Measurement and Hedging Operational Risk. Wiley.

[4] Panjer, H.H. (2006) Operational Risk: Modeling Analysis. Wiley.

http://dx.doi.org/10.1002/0470051310

[5] Franchot, A. and Roncalli, T. (2002) Mixing Internal and External Data for Managing Operational Risk. Working Paper, Groupe de Recherche Operationnelle.

[6] Shevchenko, P.V. and Wüthrich, M.V. (2006) The Structural Modeling of Operational Risk via Bayesian Inference: Combining Loss Data with Expert Opinion. The Journal of Operational Risk, 1, 3-36.

[7] Lambrigger, D.D., Shevchenko, P.V. and Wüthrich, M.V. (2007) The Quantification of Operational Risk using Internal Data, Relevant External Data and Expert Opinions. The Journal of Operational Risk, 2, 3-27.

[8] Peters, G.W., Shevchenko, P.V. and Wüthrich, M.V. (2009) Dynamic Operational Risk: Modeling Dependence and Combining Different Data Sources of Information. The Journal of Operational Risk, 4, 69-104.

[9] Chernobai, A.S., Rachev, S.T. and Fabozzi, F.J. (2007) Operational Risk: A Guide to Basel II Capital Requirements, Models, and Analysis. John Wiley and Sons, Inc.

[10] Basel Committee on Banking Supervision: Results from the 2008 Loss Data Collection Exercise for Operational Risk. Bank for International Settlement (2009). www.bis.org

[11] Allen, L., Boudoukh, J. and Saunders, A. (2005) Understanding Market, Credit and Operational Risk: The Value-atRisk Approach. Blackwell Publishing, Oxford.

[12] Cruz, M.G. (Ed.) (2004) Operational Risk Modeling and Analysis: Theory and Practice. Risk Books, London.

[13] McNeil. A.J., Frey, R. and Embrechts, P. (2005) Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press, Princeton, NJ.