Currency Barrier Option Pricing With Mean Reversion

Abstract

This paper develops a barrier-option pricing model in which the exchange rate follows a mean-reverting lognormal process. The corresponding closed-form solutions for the barrier options with time-dependent barriers are derived. The numerical results show that barrier option values and the corresponding hedge parameters under the proposed model are different from those based on the Black-Scholes model. For an up-and-out call, the mean-reverting process keeps the exchange rate in a small range around the mean level. When the mean level is below the barrier but above the strike price, the risk of the call to be knocked out is reduced and its option value is enhanced compared with the value under the Black-Scholes model. The parameters of the mean-reverting lognormal process therefore have a material impact on the valuation of currency barrier options and their hedge parameters.

Keywords: barrier options, currency options, mean-reverting process

JEL Classification: F31, G13