Generating VaR scenarios with product beta distributions

We propose a Monte Carlo simulation method to generate stress tests by VaR scenarios under Solvency II for dependent risks on the basis of observed data. This is of particular interest for the construction of Internal Models and requirements on evaluation processes formulated in the Commission Delegated Regulation. The approach is based on former work on partition-ofunity copulas, however with a direct scenario estimation of the joint density by product beta distributions after a suitable transformation of the original data.Comment: 10 pages, 25 figures, 5 table

Distortion risk measures for sums of dependent losses

We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the sum and the dependence structure of risks, represented by copulas. Our goal is to propose risk measures that take into account the fluctuations of losses and possible correlations between risk components.Comment: Accepted 25 October 2010, Journal Afrika Statistika Vol. 5, N9, 2010, page 260--26