Using a skewed exponential power mixture for value-at-risk and conditional value-at-risk forecasts to comply with market risk regulation

Samir Saissi Hassani and Georges Dionne

Abstract

We demonstrate how a mixture of two skewed exponential power distributions of the type introduced by Fernández, Osiewalski and Steel (referred to as the SEP3 density) can model the conditional forecasting of value-at-risk (VaR) and conditional value-at- risk (CVaR) to efficiently cover market risk at regulatory levels of 1% and 2.5%, as well as at the additional 5% level. Our data consists of a sample of market asset returns relating to a period of extreme market turmoil and showing typical leptokurtosis and skewness. The SEP3 mixture outcomes are benchmarked using various competing models, including the generalized Pareto distribution. Appropriate scoring functions quickly highlight valuable models, which undergo conventional backtests. As an additional backtest, we argue for and apply the CVaR part of the Patton– Ziegel–Chen optimality test to assess the conditional adequacy of CVaR. An additional aim of the paper is to present a “collaborative” framework that relies on both comparative and conventional backtesting tools, all in compliance with the recent Basel framework for market risk.