Using Skewed Exponential Power Mixture for VaR and CVaR Forecasts to Comply with Market Risk Regulation

We demonstrate how a mixture of two SEP3 densities (skewed exponential power distribution of Fernández et al., 1995) can model the conditional forecasting of VaR and 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, 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 optimality test of Patton et al. (2019) to assess the conditional adequacy of CVaR. An additional aim of this paper is to present a collaborative framework that relies on both comparative and conventional backtesting tools, all in compliance with the recent Basel regulation for market-risk