Stochastic Skew in Currency Options

We document the behavior of over-the-counter currency option prices across moneyness, maturity, and calendar time on two of the most actively traded currency pairs over the past eight years. We find that the risk-neutral distribution of currency returns is relatively symmetric on average. However, on any given date, the conditional currency return distribution can show strong asymmetry. This asymmetry varies greatly over time and often switch directions. We design and estimate a class of models that capture these unique features of the currency options prices and perform much better than traditional jump-diffusion stochastic volatility models.