Forecasting VaR and CVaR based on a skewed exponential power mixture, in compliance with the new market risk regulation

Our data, relating to a period of extreme market turmoil, show typical leptokurtosis and skewness, leading us to consider the skewed exponential power distribution of Fernández et al. (1995), referred to as the SEP3. We demonstrate that the conditional forecasting of VaR and CVaR, made up of a mixture of two SEP3 densities, can efficiently cover market risk at regulatory levels of 1% and 2.5%, as well as at the additional 5% level. The SEP3 mixture outcomes are benchmarked using a variety of competing models, including the generalized Pareto distribution. Appropriate scoring functions help focus quickly on valuable models, which should undergo five conventional backtests. As a sixth 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. Various additional statistical approaches are employed to validate models in response to Basel recommendations. We propose a novel criterion for CVaR accuracy assessment, based on its positioning in relation to the empirical CVaR‒ and 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.