Valuing path-dependent options in the variance-gamma model by Monte Carlo with a gamma bridge

Abstract

The Variance-Gamma model has analytical formulae for the values of European calls and puts. These formulae have to be computed using numerical methods. In general, option valuation may require the use of numerical methods including PDE methods, lattice methods, and Monte Carlo methods. We investigate the use of Monte Carlo methods in the Variance-Gamma model. We demonstrate how a gamma bridge process can be constructed. Using the bridge together with stratified sampling we obtain considerable speed improvements over a plain Monte Carlo method when pricing path-dependent options. The method is illustrated by pricing lookback, average rate and barrier options in the Variance-Gamma model. We find the method is up to around 400 times faster than plain Monte Carlo. ∗Corresponding author. Claudia Ribeiro gratefully acknowledges the support of Fundacao para a Ciencia e a Tecnologia and Faculdade de Economia, Universidade do Porto. The paper has benefited from comments from Lynda McCarthy.