Applications of Fuzzy Measures, Continuous Fuzzy Stochastic Processes to Pricing Put and Call Options

Abstract

Fuzzy random variables were studied by Puri and Ralescu [1] which was used by Yoshida [2] in the eld of Mathematical Finance. Since then, several researchers (to cite a few, [3], [4], [5], [6], [7], [8], [9], [10]) use fuzzy set theory application to Mathematical Finance. Later, he ([2], [10], [11]) applied fuzzy binomial tree model based on Cox et al. [12] approach to study fuzzy options pricing models. He used the same in both discrete and continuous time fuzzy stochastic process wherein put and call option prices, the stock prices are assumed to be fuzzy in nature described using non-overlapping type of triangular fuzzy numbers. While the jump factors and the interest rate involved in his model are taken as crisp. In the continuous case, he employed discrete time approximation of the number of time steps n in the binomial tree model, large and crisp continuously compounded risk-free interest rate. The main idea of this work is to explore applications of fuzzy risk- neutral probability measures involving continuously compounded fuzzy risk-free interest rate described by GLOFN to fuzzy put option and call option models. We substantiate the same to Microsoft Corporation (MSFT) shares considered from the website "www.optionistics.com" using three-period fuzzy binomial tree model.