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
, 862-876. doi: 10.4236/am.2014.56082
 Shevchenko, P.V. (2011) Modeling Operational Risk Using Bayesian Inference. Springer-Verlag Publishing Company. http://dx.doi.org/10.1007/978-3-642-15923-7
 King, J.L. (2001) Operational Risk Measurement and Modeling. Wiley.
 Cruz, M.G. (2002) Modeling, Measurement and Hedging Operational Risk. Wiley.
 Panjer, H.H. (2006) Operational Risk: Modeling Analysis. Wiley. http://dx.doi.org/10.1002/0470051310
 Franchot, A. and Roncalli, T. (2002) Mixing Internal and External Data for Managing Operational Risk. Working Paper, Groupe de Recherche Operationnelle.
 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.
 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.
 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.
 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.
 Basel Committee on Banking Supervision: Results from the 2008 Loss Data Collection Exercise for Operational Risk. Bank for International Settlement (2009). www.bis.org
 Allen, L., Boudoukh, J. and Saunders, A. (2005) Understanding Market, Credit and Operational Risk: The Value-atRisk Approach. Blackwell Publishing, Oxford.
 Cruz, M.G. (Ed.) (2004) Operational Risk Modeling and Analysis: Theory and Practice. Risk Books, London.
 McNeil. A.J., Frey, R. and Embrechts, P. (2005) Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press, Princeton, NJ.