Valuing foreign currency options with a mean‐reverting process: a study of Hong Kong dollar

Abstract

AbstractThe theoretical prediction on targeted exchange rates expects mean reversion of the exchange rates. There is some empirical evidence to support this prediction. This paper presents a model for valuing European foreign exchange options in which the forward foreign exchange rate follows a mean‐reverting lognormal process. The corresponding closed‐form solutions for the option valuation are derived. The mean‐reverting process has material impact on the foreign exchange rate option values and their hedge parameters. This tends to decrease the value of a simple put or call. On the other hand, the process also keeps the exchange rate in a small range around the mean level. As this is the region in which an option's intrinsic value is high because of the level of its strike price, there is also a tendency for option values to be enhanced compared with the values of the Black–Scholes model. The numerical results using the forward exchange rates of the Hong Kong dollar and market data of their options show that both of these effects are important for the realistic choices of parameter values. As the dynamics of targeted exchange rates may not follow the standard lognormal process as described by the Black–Scholes model, the mean‐reverting option‐pricing model may be considered for the valuation of options and estimation of associated hedge parameters on targeted exchange rates. Copyright © 2007 John Wiley & Sons, Ltd.