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...

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...

We model the new quantitative aspects of market risk management for banks that Basel established in 2016 and came into effect in January 2019. Market risk is measured by Conditional Value at Risk (CVaR) or Expected Shortfall at a confidence level of 97.5%. The regulatory backtest remains largely...

We study a class of backtests for forecast distributions in which the test statistic is a spectral transformation that weights exceedance events by a function of the modeled probability level. The choice of the kernel function makes explicit the user's priorities for model performance. The class...

Quantitative investment strategies are often selected from a broad class of candidate models estimated and tested on historical data. Standard statistical technique to prevent model overfitting such as out-sample back-testing turns out to be unreliable in the situation when selection is based on...

Patton and Timmermann (2011, 'Forecast Rationality Tests Based on Multi-Horizon Bounds', Journal of Business & Economic Statistics, forthcoming) propose a set of useful tests for forecast rationality or optimality under squared error loss, including an easily implemented test based on a...