On Jump Processes in the Foreign Exchange and Stock Markets

This article investigates the existence of discontinuities in the sample path of exchange rates and of a stock market index. Maximum-likelihood estimation of a mixed jump-diffusion process reveals that exchange rates exhibit systematic discontuinities, even after allowing for conditional heteroskedasticity in the diffusion process. The results are much more significant in the foreign exchange market than in the stock market, which suggests differences in the structure of these markets. Finally, this jump component is shown to explain some of the empirically observed mispricings in the currency options market.