Pricing Foreign Currency and Cross-Currency Options Under GARCH

Posted: 25 Aug 1998

See all articles by Jin-Chuan Duan

Jin-Chuan Duan

National University of Singapore (NUS) - Business School and Risk Management Institute

Jason Zhanshun Wei

University of Toronto - Rotman School of Management

Abstract

This paper generalizes the GARCH option pricing methodology in Duan (1995, Mathematical Finance) to a two-country setting. Specifically, we assume a bivariate nonlinear GARCH system for the exchange rate and the foreign asset price, and generalize the local risk-neutral valuation relationship in Duan (1995). We derive the equilibrium GARCH processes for the exchange rate and the foreign asset price in the two-country economy. Foreign currency options and cross-currency options can then be valued using the well-known risk-neutral valuation technique. Our setup allows rich empirical regularities such as stochastic volatility, fat tails, and the so-called leverage effect. We also run simulations to price quanto options and find that when the true environment is GARCH a constant variance model is not reliable in most cases. The proposed equilibrium valuation framework to price foreign currency and cross-currency options is the first of its kind in the literature.

JEL Classification: C10, F31, G13

Suggested Citation

Duan, Jin-Chuan and Wei, Jason Zhanshun, Pricing Foreign Currency and Cross-Currency Options Under GARCH. Journal of Derivatives, Vol. 7, No. 1, pp. 51-63, 1999, Available at SSRN: https://ssrn.com/abstract=6683

Jin-Chuan Duan

National University of Singapore (NUS) - Business School and Risk Management Institute ( email )

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Jason Zhanshun Wei (Contact Author)

University of Toronto - Rotman School of Management ( email )

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