Fast Pricing of American Options Under Variance Gamma

We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process that is constructed by replacing the calendar time with the gamma time in a Brownian motion with drift, resulting in a time-changed Brownian motion. In the case of the Black–Merton–Scholes model, there exist fast approximation methods for pricing American options. However, these methods cannot be used for the variance gamma model. We develop a new fast and accurate approximation method – inspired by the quadratic approximation – to get rid of the time steps required in finite-difference and simulation methods, while reducing error by making use of a machine learning technique on precalculated quantities. We compare the performance of our method with those of the existing methods and show that our method is efficient and accurate in the context of practical use.