Foreign Currency Option Pricing with Both Fixed and Proportional Transaction Costs

In this paper, we provide a systematic treatment of the utility based foreign currency option pricing approach in markets with both fixed and proportional transaction costs. Option prices are computed numerically in a Markov chain approximation for the case of exponential utility. This results in four boundaries: the upper boundary and lower boundary of no transaction region, the upper boundary and lower boundary of target region. Numerical results show that, the option price is an increasing function of aversion parameter, while for low values of risk aversion parameter, the option price bounds are virtually independent of the alternative risk aversion parameter.