RIDING WITH THE FOUR HORSEMEN AND THE MULTIVARIATE NORMAL TEMPERED STABLE MODEL

Abstract

In this paper, we study a model that captures four stylized facts about multivariate financial time series of equity returns: heavy tails, negative skew, asymmetric dependence, and volatility clustering (the four horsemen). The model is based on the multivariate normal tempered stable (MNTS) distribution, defined as the normal mean-variance mixture with a univariate tempered stable mixing distribution. To estimate the model, we propose a simple expectation–maximization maximum likelihood estimation procedure combined with the classical fast Fourier transform. The estimation algorithm is numerically reliable, and can be potentially used with a large number of assets. The method is applied to fit a five- and a 30-dimensional series of stock returns and to evaluate widely known portfolio risk measures. We analyzed the MNTS model with and without modeling the volatility clustering effect and compare the results with different models based on the multivariate normal and the multivariate generalized hyperbolic model.