Modelling Exchange Rates in Continuous Time: Theory, Estimation and Option Pricing

Recent research on contingent claims valuation has assumed increasingly general models of the behavior of cash securities. Relatively few attempts have been made to implement and evaluate such models empirically, however. In this paper we apply a multi-factor, continuous time pricing model to foreign exchange and interest rate data for five countries. The model allows for: (i) stochastic volatility, (ii) non-diversifiable jump risk, and (iii) stochastic interest rates. Using simulations, we examine the significance of different features of the model for option pricing. We conclude that, at least for our data set, jumps and stochastic volatility have little impact on option pricing, if one knows the average volatility over the life of the option. However, the inclusion and precise specification of stochastic interest rates are surprisingly important.