Exchange Rate Volatility and the Forward Premium Anomaly

Existing research has yet to identify a risk premium that reconciles the empirical properties of exchange rate returns with prices of other assets in financial markets. One such empirical property that has eluded pricing models is the forward premium anomaly: the tendency for currencies with high interest rates to appreciate against currencies with lower interest rates. I examine the forward premium anomaly through the lens of an arbitrage-free model for the exchange rate and term structures of interest rates in two currencies. I use the model to examine two sets of currency pairs: the U.S. Dollar and British Pound, and the U.S. Dollar and Euro. Previous papers in this literature have failed to match exchange rate volatility in their models, which is a vital component of the risk premium in exchange rate returns. I estimate the model with the joint time-series of swap rates in both relevant currencies, exchange rate returns, and prices of at-the-money exchange rate options. I include option prices because they are highly sensitive to the level of volatility and to the pricing of volatility risk. When I use options to estimate the model, it successfully captures both exchange rate volatility and the term structure of interest rates in both currencies. Using simulated data, I show that the model also replicates the empirical findings in Fama (1984) and is consistent with the forward premium anomaly.