A simple normal inverse Gaussian-type approach to calculate value-at-risk based on realized moments

ABSTRACT Expanding the realized variance concept through realized skewness and kurtosis is a straightforward process. We calculate one-day forecasts for these moments with a simple exponentially weighted moving average approach. Once the forecasts are computed, we apply them in a method of moments to fit a sophisticated distribution. The normal inverse Gaussian distribution is appropriate for this purpose because it exhibits higher moments, and a simple analytical solution for the method of moments exists. We then calculate the value-at-risk for the Deutsche Aktienindex (DAX) using this technique. Although the model is comparatively simple, the empirical analysis shows good results in terms of backtesting.