On jump processes in the foreign exchange and stock markets

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