On the numerical evaluation of option prices in the variance gamma model

Abstract

Because the pricing equations in Levy models contain integrals, it is difficult to develop rapid numerical methods for solving them. Although the integrals are not periodic, the standard evaluation methods use the FFT, and therefore require large computational regions to ensure accuracy. In earlier work, we developed efficient methods for pricing options in the Merton and Kou double exponential models. The methods rely on the fact that in those models the density functions satisfy ordinary or partial differential equations, so differential methods can be used to evaluate the integrals. In this paper, we present effective numerical methods for pricing options in another Levy model, the Variance Gamma model.

Keywords:

• option pricing
• variance gamma