IJAM, Volume 28, No. 1 (2015)

Abstract. We develop a lattice-based model to evaluate European and American plain vanilla options when the underlying asset price is driven by a variance gamma process. By applying the L\'{e}vy-It\^{o} decomposition of the process, we obtain a compound Poisson process made up of a linear drift and the sum of the jumps taken by the process. A multinomial lattice is derived to approximate the compound Poisson process and is used as the corner stone to approximate the evolution of a certain asset price. European and American options are evaluated and, because numerical results show monotonic convergence at the rate of $1/n$, we apply a simple two-point Richardson extrapolation and obtain a fast and accurate pricing model.