A comparison of risk aggregation estimates using copulas and Fleishman distributions

Determining banks' expected losses (EL) is straightforward because they are calculated using a linear combination of credit risk-related measures. Non-linear metrics, like economic capital (EC), pose considerable implementation challenges including computation complexity and a lack of adequate risk aggregation and attribution techniques when multiple portfolios and/or product segmentations are involved. Copulas have been used to overcome these problems, but the Fleishman procedure, which uses a polynomial transformation to generate non-normal data, may provide a more tractable alternative. In this article, EC simulation estimates using the extended (multivariate) Fleishman method and the Gumbel copula are compared. The Fleishman approach is found to be easier to implement than the Gumbel approach and provides comparable results when the correlation and concordance between losses are low. The Fleishman method preserves the first four moments and two measures of dependence (Pearson's rho and Kendal's tau); the copula approach preserves only the first two moments of the empirical loss distributions.