Fuzzy pricing of geometric Asian options and its algorithm

Abstract

Owing to the fluctuations of the financial market, input data in the options pricing formula cannot be expected to be precise. This paper discusses the problem of pricing geometric Asian options under the fuzzy environment. We present the fuzzy price of the geometric Asian option under the assumption that the underlying stock price, the risk-free interest rate and the volatility are all fuzzy numbers. This assumption makes the financial investors to pick any geometric Asian option price with an acceptable belief degree. In order to obtain the belief degree, the interpolation search algorithm has been proposed. Some numerical examples are presented to illustrate the rationality and practicability of the model and the algorithm. Finally, an empirical study is performed based on the real data. The empirical study results indicate that the proposed fuzzy pricing model of geometric Asian option is a useful tool for modeling the imprecise problem in the real world.