The pricing of compound option under variance gamma process by FFT

Cuixiang Li, Huili Liu, Mengna Wang and Wenhan Li

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 24, 6122-6136

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.

Date: 2021
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DOI: 10.1080/03610926.2020.1740268

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