Multivariate heavy-tailed models for Value-at-Risk estimation

For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's $t$ distributions allowing different marginals to have different indices of tail thickness. After a discussion of relevant estimation and simulation issues, we conduct a backtesting study on a set of portfolios containing derivative instruments, using historical US stock price data.