Abstract This paper introduces the moment interaction between different assets in the semi-nonparametric modeling of a multivariate distribution. We analyze bivariate portfolios where skewness and kurtosis may interact between different assets, showing that these new parameters may be significant pieces of information, particularly for measuring risk. Model performance for risk assessment is tested with backtesting techniques considering equally weighted portfolios of the S&P 500 and Nasdaq 100 indices and major cryptocurrencies (Bitcoin and Ethereum), the latter with high-frequency data. The results show adequate performance in terms of Value-at-Risk, Median Shortfall, and Expected Shortfall, especially for high confidence levels.
Jiménez et al. (Thu,) studied this question.