Multinomial method for option pricing under Variance Gamma

TL;DR

This paper introduces a multinomial approximation method for option pricing under the Variance Gamma process, enabling efficient valuation of American and Bermudan options with comparable accuracy to existing methods.

Contribution

It develops a discrete Markov chain approximation matching the first four cumulants of the Variance Gamma process, facilitating practical option pricing.

Findings

The multinomial method accurately prices European options.

The approach effectively prices American options with comparable results to finite difference methods.

Numerical results align well with Black-Scholes and other benchmark models.

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 discrete time Markov chain with the same firsts four cumulants. This approach is particularly convenient for pricing American and Bermudan options, which can be exercised at any time up to 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 model.