A Bayesian Approach to Modeling Operational Risk When Data is Scarce
Abstract: The goal of this thesis is to investigate whether it is possible to construct an advanced measurement approach (AMA) model for operational risk when the number of internal data points are very scarce. An AMA model should combine internal data, external data, scenario data, and business environment and internal control factors to give a one year VaR estimate with 99.9 % confidence of operational risk. Out of the methods of combining the different data sources suggested in the literature, only the Bayesian inference approach is suitable due to the small amount of data available. In order to not be restricted to suitable conjugate-pairs, a numerical approach to evaluating the posterior distributions is undertaken, and three different severity distributions are tried out. The distributions tried are the Weibull; the generalized Champernowne, which is suggested by the literature due to its tail behavior; and the g-and-h, which is suggested by the literature due to both its versatility and tail behavior. The conclusion of this thesis is that it is possible to construct an AMA model with Poisson loss frequencies using Bayesian inference to combine the different data sources. However, the data material was too scarce to draw any reliable conclusions about the severity distribution.
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