The main objective of this paper is to propose an alternative valuation framework for pricingforeign currency and cross-currency options, which is capable of accommodating existing empiricalregularities. 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 rateand the foreign asset price, and generalize the local risk-neutral valuation principle for pricingderivatives. We define an equilibrium price measure in the two-country economy and derive thelocally risk-neutralized GARCH processes for the exchange rate and the foreign asset price. Foreigncurrency options and cross-currency options are then valued using Monte Carlo simulations. Oursetup accommodates rich empirical regularities such as stochastic volatility, fat tailed distributionsand leverage effect extensively documented for financial data series. Numerical results show thatour proposed model exhibits properties that are consistent with the documented empirical regularitiesfor foreign currency options and quanto options.