This thesis aims to investigate the dynamic process of currency jump risks and applies it to pricing currency options. We explore a Markov-modulated jump diffusion model with state-dependent jump risks (MS-MJ model), which incorporates jump intensity and state-dependence to capture the characteristics of cyclical movements and abnormal shock. Comparing the G-10 currencies (EUR, GBP, JPY, CAD, CHF, AUD, NOK, NZD and SEK) against the USD, the empirical results found that the G-10 currencies are characterized by business cycles and state-dependent jump risks. Moreover, our findings suggest that incorporating state-dependence in jump risks can improve model fitting and option pricing. The sample observations show the MS-MJ model can be more suitable with most of the G-10 spot FX rates, and can improve the pricing performance on most of the G-10 currency options, in particular for at-the-money options.
