If a probability distribution is sufficiently close to a normal distribution, its density can be approximated by the truncated Gram-Charlier series where skewness and kurtosis directly appear as parameters. However, the existing literature is restricted to truncating the series expansion until...

In this paper, we study the skewness risk and its return predictability in the energy market. Skewness risk is often used to measure the possibility of market crash. We study both physical skewness (market skewness and cross-sectional average realized skewness) estimated from underlying stock...

Variance swaps are natural instruments for investors taking directional bets on volatility and are often used for portfolio protection. But the crucial observation suggests that derivative professionals may desire to hedge beyond volatility risk and there exists the need to hedge higher-moment...