Geometric Brownian Motion Assumption and Generalized Hyperbolic Distribution on Modeling Returns

Abstract

Generalized hyperbolic distribution and some of its subclasses like normal, hyperbolic and variance gamma distributions are used to fit daily log returns of eight listed companies in Nairobi Securities Exchange and Montréal Exchange. EM-based maximum likelihood estimation procedure is used to estimate parameters of the model. Kernel densities and empirical distribution of data are compared. The goodness of fit statistics of proposed distributions are used to measure how well model fits the data. Empirical results show that Generalized hyperbolic Distribution seems to improve partially, the geometric Brownian assumption on modeling returns of the underlying process, both in a developed and emerging market. Both markets seem to have different stochastic time.