TITLE:
An Application of Bayesian Inference on the Modeling and Estimation of Operational Risk Using Banking Loss Data
AUTHORS:
Kashfia N. Rahman, Dennis A. Black, Gary C. McDonald
KEYWORDS:
Monte Carlo Simulation, Value-at-Risk, Basel II, Operational Risk, Bayesian
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.6,
April
2,
2014
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.