Pricing Asian options using fuzzy sets theory

Abstract

This paper studies the valuation of Asian options with fuzzy sets theory. In order to overcome the problem of imprecise parameters under uncertain environment, we introduce the fuzzy underlying asset price, fuzzy interest rate, fuzzy dividend rate and fuzzy volatility to establish a fuzzy pricing model for Asian options. The fuzzy price formula for the European continuous geometric vanilla Asian option and fuzzy approximate price formula for its corresponding arithmetic Asian option are then obtained. These formulas are more flexible and subsume the results of the crisp models as their special cases. Numerical results show that the proposed fuzzy pricing model can be used to help the investor choose a suitable Asian option price with an acceptable belief degree for the later use.