According to Doowoo Nam (2013), VaR of non-normal portfolio returns approximated by g-and-h distribution can be decomposed pretty much in the same way as the VaR of a portfolio with normal returns. After the estimation of the four g-and-h parameters for the non-normal portfolio, Nam shows that VaR contribution of an individual asset can be determined using Euler's homogeneous function theorem. The result is interesting since it seems to provide more reliable way to estimate VaR for strongly skewed returns than the Cornish-Fischer expansion based approach.
However, I'm little confused how this decomposition, which is based on the Beta between the asset and the portfolio, takes into account the co-skewness and co-kurtosis of the individual asset and the portfolio. Rather it seems that the decomposition is only based on covariance. Could anyone elucidate this interesting result?