Abstract
According to the last proposals of the Basel Committee on Banking Supervision, banks or insurance companies under the advanced measurement approach (AMA) must use four different sources of information to assess their operational risk capital requirement. The fourth includes ’business environment and internal control factors’, i.e., qualitative criteria, whereas the three main quantitative sources available to banks for building the loss distribution are internal loss data, external loss data and scenario analysis. This paper proposes an innovative methodology to bring together these three different sources in the loss distribution approach (LDA) framework through a Bayesian strategy. The integration of the different elements is performed in two different steps to ensure an internal data-driven model is obtained. In the first step, scenarios are used to inform the prior distributions and external data inform the likelihood component of the posterior function. In the second step, the initial posterior function is used as the prior distribution and the internal loss data inform the likelihood component of the second posterior function. This latter posterior function enables the estimation of the parameters of the severity distribution that are selected to represent the operational risk event types.
Highlights
Basel II capital accord defines the capital charge as a risk measure obtained on an annual basis at a given confidence level on a loss distribution that integrates the following four sources of information: internal data, external data, scenario analysis, business environment and internal control factors
The Range of Practice Paper recognises that “there are numerous ways that the four data elements have been combined in advanced measurement approach (AMA) capital models and a bank should have a clear understanding of the influence of each of these elements in their capital model”
This paper presents an intuitive approach to building the loss distribution function using the Bayesian inference framework and combining the different regulatory components
Summary
Basel II capital accord defines the capital charge as a risk measure obtained on an annual basis at a given confidence level on a loss distribution that integrates the following four sources of information: internal data, external data, scenario analysis, business environment and internal control factors (see Box 1). Our Bayesian cascade approach can be a viable alternative when available internal data is not numerous, in which the risk profile has some similarities with the entities providing the external data and in which the scenarios are only characterised by a few points evaluated by expert judgement for a given set of likelihoods. In the situation considered in this paper, the three elements did not have the same characteristics, external data were only collected above a high threshold, scenarios were only representing by a few points in the right tail of the distributions underpinning quantifications and internal data were collected above different thresholds depending on the type of risks.
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