Problem of pricing American Fuzzy Put Option Buyer’s Model for general Trapezoidal Fuzzy Numbers

Abstract

Fuzzy American put option pricing in both discrete and continuous time by using fuzzy random variables and fuzzy expectation based on the decision maker's subjective judgement was studied by Yoshida. American Fuzzy Put Option Model (AFPOM) based on fuzzy risk-neutral probability measure was defined by Muzzioli and Reynaerts using non-overlapping trapezoidal fuzzy numbers. In this study, we introduce a new fuzzy risk-neutral probability measure for a more general class of trapezoidal fuzzy numbers that could be overlapping or non-overlapping. Using the same, we define fuzzy martingale, fuzzy super martingale and fuzzy submartingale of the discrete time fuzzy stochastic process described by fuzzy random variables. We also define prices in AFPOM with respect to the filtration. AFPOM for future contracts is also introduced. Using the data, we discuss the profit and loss values of buyers of AFPOM for future contracts and proved that the maximum profit obtained by the buyers of AFPOM using general trapezoidal fuzzy numbers is optimal.

Keywords: AFPOM prices, fuzzy future prices, new fuzzy risk-neutral probability measure, general trapezoidal fuzzy numbers.

Cite this Article

K. Meenakshi, Felbin C. Kennedy. Problem of Pricing American Fuzzy Put Option Buyer’s Model Involving General Trapezoidal Fuzzy Numbers. Recent Trends in Parallel Computing. 2019; 6(1): 27–37p.