Crash Risk in Currency Returns

Abstract

We quantify crash risk in currency returns. To accomplish this task, we develop and estimate an empirical model of exchange rate dynamics using daily data for four currencies relative to the US dollar: the Australian dollar, the British pound, the Swiss franc, and the Japanese yen. The model includes (i) normal shocks with stochastic variance, (ii) jumps up and down in the exchange rate, and (iii) jumps in the variance. We identify these components using data on exchange rates and at-the-money implied variances. We find that the probability of an upward (downward) jump in the exchange rate, associated with depreciation (appreciation) of the US dollar, is increasing in the domestic (foreign) interest rate. The probability of jumps in variance is increasing in the variance but not related to interest rates. Many of the jumps in exchange rates are associated with macroeconomic and political news, but jumps in variance are not. On average, jumps account for 25% (and can be as high as 40%) of total currency risk, as measured by the entropy of exchange rate changes, over horizons of one to three months. Preliminary analysis suggests that these properties of currency returns correspond to observed option smiles and that jump risk is priced.