Jumps, Martingales, and Foreign Exchange Futures Prices

A common specification about the behavior of foreign exchange spot and futures prices is that they follow continuous diffusion processes. The empirical regularities uncovered from daily and weekly currency futures data, however, cast doubts on the validity of this model. First, contrary to the suggestions in the literature, changes in foreign currency futures prices are serially correlated; variance ratio tests and other related tests overwhelmingly reject Samuelson's martingale hypothesis. Second, foreign exchange futures prices do not appear to have continuous sample path; the evidence suggests the presence of a jump component, which may lead to pricing bias when applying the standard Black-Scholes option pricing formula to foreign exchange markets.