Does implied volatility of currency futures option imply volatility of exchange rates?

By investigating currency futures options, this paper provides an alternative economic implication for the result reported by Stein [Overreactions in the options market, Journal of Finance 44 (1989) 1011-1023] that long-maturity options tend to overreact to changes in the implied volatility of short-maturity options. When a GARCH process is assumed for exchange rates, a continuous-time relationship is developed. We provide evidence that implied volatilities may not be the simple average of future expected volatilities. By comparing the term-structure relationship of implied volatilities with the process of the underlying exchange rates, we find that long-maturity options are more consistent with the exchange rates process. In sum, short-maturity options overreact to the dynamics of underlying assets rather than long-maturity options overreacting to short-maturity options.