Exchange Rate Dynamics With Crash Risk and Interventions

An exchange rate model with crash risk is developed with the exchange rate confined in a wide moving band. A currency crash occurs when its exchange rate breaches a boundary. Using an asymmetric mean-reverting fundamental shock to incorporate intervention policy in the model, the log-normalised exchange rate follows a mean-reverting square-root process, which generates left-skewed exchange rate distributions consistent with outlier negative returns in carry trades. The exchange rates of nine major currencies against the US dollar can be calibrated according to the model, where the mean reversion in the exchange rate dynamic is negatively cointegrated with the risk reversals