Valuing Foreign Currency Options with a Mean-Reverting Process: A Study of Hong Kong Dollar

The theoretical prediction of target exchange rates expects mean reversion of the exchange rates. 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 mean-reverting process has material impact on the foreign exchange rate option values and their hedge parameters. The numerical results using the forward exchange rates of the Hong Kong dollar and market data of their options show such impact. As the dynamics of target 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 valuation of options and estimation of associated hedge parameters on target exchange rates.