A simple approach to valuing Asian rainbow options

Abstract

Asian rainbow options, also called options on the minimum or the maximum of two or several average prices, are found widely applicable in both risk management and the design of incentive contracts for executive compensation. However, their valuation is very complicated. This paper proposes a new and simple approach to valuing such options on dividend-paying assets. Starting from an observation that the price of an Asian option in some cases can become that of a vanilla European option and then using the method of Johnson (1987), we can easily obtain a closed-form valuing formula for the option with two geometric averaging. Moreover, this method can be directly extended to obtain a closed-form solution for the case of several geometric averaging. We also derive a closed-form approximation pricing formula for an Asian rainbow option with two arithmetic averaging based on the obtained price formula of its counterpart geometric averaging Asian rainbow option and the approach of Zhang (1998). Numerical comparison shows the efficiency and accuracy of our approximation price and the different effects of the interest rate, volatility, dividend and observation frequency on the price of Asian rainbow options.