Multivariate Generalized Hyperbolic Regression: Estimation and Application

From the past experiences, it is obviously perceived that the empirical distributions of market data are heavy tailed and highly skewed which make it difficult to fit the distributions to the data. Although Generalized Hyperbolic (GH) distributions have been previously applied in the modeling of market data, the effect of external factors on the distributional parameters is not included. The aim of this paper is to introduce the multivariate generalized hyperbolic regression to estimate the parameters of GH distributions when the location and skewness parameters are under the influence of external factors. The proposed model is used for the first time in statistical and financial literature research. We use 1769 daily returns from January 2000 to January 2007 of five Swiss blue chips. In the proposed model, the EM algorithm is used to estimate the parameters.