Portfolio VaR for SNP distributions

摘要

This paper compares the traditional method of calculating portfolio Value-at-Risk (VaR) under the Gaussian distribution to the risk measures provided by using the Semi-Nonparametric (SNP) approach based on Gram-Charlier expansions. The main advantage of the latter method is the fact that it accurately approximates the true density of the portfolio by a sufficiently large expansion and involves a flexible parametric representation capable of featuring the salient empirical regularities of financial data. We show that the multivariate Gram-Charlier specification of the type provided in [1] allows the estimation of the time varying variance-covariance structure of the portfolio consistently with the SNP approach and that Gram-Charlier densities admit a straightforward method for quantile computation. We compare the performance of the VaRs obtained for different bivariate portfolios finding a clear underestimation (overestimation) of VaR measures for the traditional Gaussian (Student's t based) methods compared to our SNP approach.