Pricing 'partial-average' Asian options with the binomial method

Abstract

An Asian option is path-dependent derivatives whose payoff depends on the average of the underlying asset price over a certain pre-specified period of time. There is no simple closed-form solution for arithmetic Asian option hence the development of efficient and accurate numerical methods has become critical. In this paper, a modified binomial method is presented for pricing a more common arithmetic Asian option, by averaging the asset between two time periods in the life span of the option. This option is called the 'partial-average' Asian option. Subsequently, the representative averages are used instead of the actual ones for pricing the option. The set of representative averages is constructed first by determining the maximum and the minimum averages, where other averages are calculated by dividing equally the distance between the maximum and the minimum averages. For Asian option with average strike, if the distance between two time periods is widened by shifting the second time period to the right then the price becomes lower. But if the distance is widened by shifting the first time period to the left then the price becomes higher. The algorithm is not only simple but also easy to implement.