Volatility, Momentum, and Time-Varying Skewness in Foreign Exchange Returns

Abstract

This article tests a stochastic volatility model of exchange rates that links both the level of volatility and its instantaneous covariance with returns to pathwise properties of the currency. In particular, the model implies that the return–volatility covariance behaves like a weighted average of recent returns and hence switches signs according to the direction of trends in the data. This implies that the skewness of the finite-horizon return distribution likewise switches sign, leading to time-varying implied volatility “smiles” in options prices. The model is fit and assessed using Bayesian techniques. Some previously reported volatility results are accounted for by the fitted models. The predicted pattern of skewness dynamics accords well with that found in historical options prices.