Implementing Loss Distribution Approach for Operational Risk

To quantify the operational risk capital charge under the current regulatory framework for banking supervision, referred to as Basel II, many banks adopt the Loss Distribution Approach. There are many modeling issues that should be resolved to use the approach in practice. In this paper we review the quantitative methods suggested in literature for implementation of the approach. In particular, the use of the Bayesian inference method that allows to take expert judgement and parameter uncertainty into account, modeling dependence and inclusion of insurance are discussed

Isotropic spectral additive models of the covariogram

A class of additive covariance models of an isotropic random process is proposed, motivated by the spectral representation of the covariance function. Model parameters are estimated by using a special case of the minimum norm quadratic estimation estimator, whose asymptotic moments have convenient expressions in terms of spectral densities. Fitting a model in this class is equivalent to fitting an additive model of the spectral density. The class of spectral additive models proposed is dense in the set of summable covariance functions having a spectral density, allowing approximately unbiased estimation of an arbitrary covariance function and its spectral density. Theoretical results are supported by numerical comparison with commonly used models. A procedure to assist model selection is proposed. The techniques are illustrated with an application to contaminant data. Copyright (c) 2008 Royal Statistical Society.