Risk estimation using the multivariate normal inverse Gaussian distribution

Abstract

Appropriate modeling of time-varying dependencies is very important for quantifying financial risk, such as the risk associated with a portfolio of financial assets. Most of the papers analyzing financial returns have focused on the univariate case. The few that are concerned with their multivariate extensions are mainly based on the multivariate normal assumption. The idea of this paper is to use the multivariate normal inverse Gaussian (MNIG) distribution as the conditional distribution for a multivariate GARCH model. The MNIG distribution belongs to a very flexible family of distributions that captures heavy tails and skewness in the distribution of individual stock returns, as well as the asymmetry in the dependence between stocks observed in financial time series data. The usefulness of the MNIG GARCH model is highlighted through a value-at-risk (VAR) application on a portfolio of European, American and Japanese equities. Backtesting shows that for a one-day holding period this model outperforms a Gaussian GARCH model and a Student’s t GARCH model. Moreover, it is slightly better than a skew Student’s t GARCH model.