The Variance Gamma (VG) Model with Long Range Dependence

Abstract

This thesis mainly builds on the Variance Gamma (VG) model for financial assets over time of Madan & Seneta (1990) and Madan, Carr & Chang (1998), although the model based on the t distribution championed in Heyde & Leonenko (2005) is also given attention. The primary contribution of the thesis is the development of VG models, and the extension of t models, which accommodate a dependence structure in asset price returns. In particular it has become increasingly clear that while returns (log price increments) of historical financial asset time series appear as a reasonable approximation of independent and identically distributed data, squared and absolute returns do not. In fact squared and absolute returns show evidence of being long range dependent through time, with autocorrelation functions that are still significant after 50 to 100 lags. Given this evidence against the assumption of independent returns, it is important that models for financial assets be able to accommodate a dependence structure.