Pricing Foreign Currency and Cross-Currency Options Under GARCH

The main objective of this paper is to propose an alternative valuation framework for pricing foreign currency and cross-currency options, which is capable of accommodating existing empirical regularities. The paper generalizes the GARCH option pricing methodology of Duan (1995) 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 principle for pricing derivatives. We define an equilibrium price measure in the two-country economy and derive the locally risk-neutralized GARCH processes for the exchange rate and the foreign asset price. Foreign currency options and cross-currency options are then valued using Monte Carlo simulations. Our setup accommodates rich empirical regularities such as stochastic volatility, fat tailed distributions and leverage effect extensively documented for financial data series. Numerical results show that our proposed model exhibits properties that are consistent with the documented empirical regularities for foreign currency options and quanto options.