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arXiv · 1903.07519

A fast method for pricing American options under the variance gamma model

Weilong Fu·Ali Hirsa
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Abstract

We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift, which makes it a time-changed Brownian motion. In general, the finite difference method and the simulation method can be used for pricing under this model, but their speed is not satisfactory. So there is a need for fast but accurate approximation methods. In the case of Black-Merton-Scholes model, there are fast approximation methods, but they cannot be utilized for the variance gamma model. We develop a new fast method inspired by the quadratic approximation method, while reducing the error by making use of a machine learning technique on pre-calculated quantities. We compare the performance of our proposed method with those of the existing methods and show that this method is efficient and accurate for practical use.

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Weilong Fu, Ali Hirsa. 2019-03-18. A fast method for pricing American options under the variance gamma model. https://doi.org/10.21314/jcf.2021.002

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