Has the interaction between skewness and kurtosis of asset returns information content for risk forecasting?

This paper introduces the effect of the crossed products of Hermite polynomials on Gram-Charlier densities. This allows capturing the impact of the interaction between skewness and kurtosis and evaluating this new parameter as an additional source of information for risk management. We show that our modified Gram-Charlier density presents an improved accuracy, especially at distribution tails. Risk quantification is assessed for S&P500 losses with backtesting procedures for Value-at-Risk and Median Shortfall.

Automated summary

This paper introduces the effect of crossed products of Hermite polynomials on Gram-Charlier densities and proposes an improved density function to accurately capture the distribution tails. It evaluates risk quantification for S&P500 losses using backtesting procedures for Value-at-Risk and Median Shortfall.