Pricing Currency Options with Bates Model: Analytical Tractability versus Empirical Misspeci cation

Abstract

In this thesis I complement the results from Bates (1996) wherein a Stochastic Volatility Jump-Di usion model for pricing foreign currency options is introduced and evaluated against USD/DM foreign exchange options. I complement Bates results with two di erent calibration methodologies, nonlinear least-squares and the built-in MATLAB function fmincon, using the same dataset that was used in Bates (1996). The results shows that the nonlinear least-squares calibration exhibit parameter values closely related to that of Bates (1996) and performs well when testing the pricing performance across moneyness, thus con rming Bates results. For the fmincon calibration, certain implicit parameter values are improbable given the model spec- i cation. This also corresponds to a comparatively worse pricing performance than that of lsqnonlin and an overall inconsistent pricing with respect to theoretical interpretation.