An Extreme Value Theory Approach to Calculating Minimum Capital Risk Requirements

Abstract

This paper investigates the frequency of extreme events for three LIFFE futures contracts for the calculation of minimum capital risk requirements (MCRRs). We propose a semi-parametric approach where the tails are modelled by the Generalized Pareto Distribution and smaller risks are captured by the empirical distribution function. We compare the capital requirements form this approach with those calculated from the unconditional density and from a conditional density - a GARCH(1,1) model. Our primary finding is that both in-sample and for a hold-out sample, our extreme value approach yields superior results than either of the other two models which do not explicitly model the tails of the return distribution. Since the use of these internal models will be permitted under the EC-CAD II, they could be widely adopted in the near future for determining capital adequacies. Hence, close scrutiny of competing models is required to avoid a potentially costly misallocation capital resources while at the same time ensuring the safety of the financial system.

Keywords: Minimum Capital Risk Requirements, Generalized Pareto Distribution, GARCH models

JEL Classification: C14, C15, G13