Forecasting Currency Volatility : A Comparison of Implied Volatilities and AR(FI)MA Models

Using high frequency intraday returns, we calculate the realized volatility of the USD/GBP, USD/DEM and USD/JPY exchange rates. It is shown that the dynamics of the logarithms of realized volatilities can be captured by either a fractionally integrated long memory model or a short memory ARMA model. The paper compares the forecasting properties of a short memory model, a long memory model and the implied volatilities from OTC foreign currency options, for realized volatilities over horizons ranging from one day to three months. We find that the enhanced performances of the historical forecasts, relative to implied volatilities, come from the use of high frequency returns, and not from the use of a long memory model. Both intraday models provide more accurate forecasts than implied volatilities for the one-day and one-week forecast horizons while implied volatilities perform at least as accurately as the intraday models for the one-month and three-month horizons. Significant incremental information is found in historical forecasts, relative to implied volatilities, for the one-day and one-week forecast horizons but there is no significant evidence for the one-month and three-month forecast horizons