Mathematical Biology Seminar



Tuesday, 04/02/2019, at 4:10 - 5:00








Multivariate generalized hyperbolic laws for modeling financial log-returns – empirical and theoretical considerations


Stergios Fotopoulos




Department of Finance and Management Science, WSU










The aim of this study is to analyze the multivariate generalized hyperbolic (MGH) distribution for capturing the uncertainty in financial log-returns. Beginning with the multivariate geometric subordinated Brownian motion for asset prices, we first demonstrate that the mean-variance mixing model of the multivariate normal law is natural for log-returns of financial assets. This multivariate mean-variance mixing model forms the basis for deriving the MGH family as a class of distributions for modeling the behavior of log-returns. While theory suggests MGH to be an appropriate family, empirical considerations must also support such a proposition. This article reviews various empirical criteria in support of the MGH family. From a theoretical perspective, we present an alternative form of the density for the MGH family. This alternative density form for the MGH family is more convenient for deriving an important limiting result. Numerical study on the distributional behavior of six stocks in the US market forms the foundation of investigating the suitability of the MGH family and some of its well-known sub-families. Along the way, we present the MCECM algorithm to estimate the parameters involved, together with various quantitative statistics such as mean, variance, skewness, and kurtosis. To establish goodness-of-fit results for the MGH distribution, a recently developed algorithmic procedure is adopted. The numerical study on the six stocks confirms the suitability of the MGH in different time scales for the log-returns, while the aggregated data supports the appropriateness of the multivariate normal distribution as well. 


KEY WORDS: Normal subordination; Multivariate generalized hyperbolic distributions; Kurtosis; EM algorithm; Non-Gaussian; Conditional laws. 

AMS subject classification: 60E10, 62H05, 60H10, 60G15, 60F05. 

This work is co-authored with Alex Paparas and Venkata K. Jandhyala