The pricing of compound option under variance gamma process by FFT

Abstract

In this paper, we price a compound option with log asset price following an extended variance gamma process. The extended variance gamma process can control the skewness and kurtosis. The parameters of the model are estimated via the maximum likelihood method from historical data. We start with finding the risk neutral Esscher measure under which the discounted asset price process is a martingale. Then we derive an analytical pricing formula for compound option in terms of the Fourier integral of the characteristic function of extended variance gamma process, and we use this formula, in combination with the FFT algorithm, to calculate the compound option price across the whole spectrum of the exercise price. Finally, we present some numerical results for illustration.

Keywords:

• Compound option
• variance gamma process
• Fourier transform
• Esscher transform
• FFT algorithm

Acknowledgement

We would like to thank an anonymous referee for valuable comments and suggestions which lead to the improvement of this article.

Additional information

Funding

This work was supported by the Natural Science Foundation of China (11571089, 11501164); and the Foundation of Hebei Education Department (ZD2018065, QN2019073).