Pricing Foreign Currency Options with Stochastic Volatility

Abstract

Abstract This paper investigates the consequences of stochastic volatility for pricing spot foreign currency options. A diffusion model for exchange rates with stochastic volatility is proposed and estimated. The parameter estimates are then used to price foreign currency options and the predictions are compared to observed market prices. We find that allowing volatility to be stochastic results in a much better fit to the empirical distribution of the Canada–U.S. exchange rate, and that this improvement in fit results in more accurate predictions of observed option prices. Recent attempts to use option models to price foreign currency options have been relatively disappointing. Although observed foreign currency option prices satisfy the boundary conditions that are implied by all option pricing models (Bodurtha and Courtadon (1986) ), attempts to specify models that lead to accurate point forecasts of option prices have not been very successful.