Crash Risk in Currency Returns

We develop an empirical model of bilateral exchange rates. It includes normal shocks with stochastic variance and jumps in an exchange rate and in its variance. The probability of a jump in an exchange rate corresponding to depreciation (appreciation) of the U.S. dollar is increasing in the domestic (foreign) interest rate. The probability of a jump in variance is increasing in the variance only. Jumps in exchange rates are associated with announcements; jumps in variance are not. On average, jumps account for 25% of currency risk. The dollar carry index retains these features. Options suggest that jump risk is priced.