An Extreme Value Theory Approach to Calculating Minimum Capital Risk Requirements

This article investigates the effect of modeling extreme events on the calculation of minimum capital risk requirements for three LIFFE futures contracts. The use of internal models will be permitted under the European Community Capital Adequacy Directive II and will be widely adopted in the near future for determining capital adequacies. Close scrutiny of competing models is required to avoid a potentially costly misallocation of capital resources, to ensure the safety of the financial system. The authors propose a semi‐parametric approach, for which extreme risks are modeled using a generalized Pareto distribution, and smaller risks are characterized by the empirically observed distribution function. The primary finding of comparing the capital requirements based on this approach with those calculated from both the unconditional density and from a conditional density (a GARCH(1,1) model), is that for both in‐sample and out‐of‐sample tests, the extreme value approach yields superior results. This is attributable to the fact that the other two models do not explicitly model the tails of the return distribution.