The Gram-Charlier and Cornish-Fisher expansions are tools often used to compute value at risk (VaR) in the context of skewed and leptokurtic return distributions. These approximations use the first four moments of the unknown target distribution to compute approximate distribution and quantile...

An approach to approximate the multivariate distribution of time-aggregated stock returns in the GARCH context is developed here. The approach yields a one time-step simulation procedure as opposed to a multiple time-step simulation required in such a context. For this purpose, the exact moment...