Multinomial method for option pricing under Variance Gamma

Abstract

This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a continuous time process with the same first four cumulants, and then discretized in time and space. This approach is particularly convenient for pricing American and Bermudan options, which can be exercised before the expiration date. Numerical computations of European and American options are presented, and compared with results obtained with finite differences methods and with the Black-Scholes prices.