Quanto option pricing with a jump diffusion process

Abstract

This paper proposes a dynamic model for the spot foreign exchange rate which is governed by a standard Brownian motion and a stationary compound Poisson process in the domestic-real world. Using the tool of the Esscher transform, we explore two suitable parameters for the amplitude and the intensity of the jump process and redefine the dynamic process of the spot foreign exchange rate under the domestic risk-neutral measure. Based on the above work, we obtain two types of the quanto option pricing formulas. At last, we utilize the real market data of the stock “Aluminum Corporation of China Limited” and the foreign exchange rate of USD/CNY to obtain the value of the quanto option taken the constant K₁ as the strike price in the domestic currency. Furthermore, we investigate the implied volatility of the quanto option.

Keywords:

• Quanto option pricing
• jump diffusion process
• Esscher transform
• numerical analysis

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 60H30
• Secondary 62P05

Additional information

Funding

This work was supported by the Social Science Foundation Project of Hebei Province (No. HB19YJ055).