An EM algorithm for multivariate NIG distribution and its application to value-at-risk

Many empirical studies show that the normal-inverse Gaussian (NIG) distribution allows a realistic description of asset returns. This paper deals with the maximum likelihood estimation (MLE) of parameters of the multivariate NIG (MNIG) distribution. Due to the complexity of the likelihood, direct optimization is difficult and inefficient. An expectationmaximization (EM) algorithm is proposed to compute the MLE of the MNIG parameters. This paper also deals with the Value-at-Risk (VaR) estimation for portfolio return under the MNIG distribution. In addition, a simulation study is carried out for the performance of VaR estimations, and the EM algorithm serves as an efficient way to compute portfolio VaR in the cases of the tail behavior of asset return.