Asac 2005 Conference Binomial Option Pricing Model Using O(2, 2)−trapezoidal Type Fuzzy Numbers

Decision-making problems, in general, are ill defined as several times their objectives and model parameters are not precisely known. As a result there has been growing interest in using fuzzy algebra in such models. Historically, probability theory is presented as forming theoretical foundations for reasoning and decision making in situations involving uncertainty. However, often one is faced with the situations in which decisions are required to be made on the basis of illdefined variables, and imprecise (vague) data. Fuzzy algebra is a simple and potentially a useful way to propagate impreciseness through a cascade of calculations. It has been used to model systems that are hard to define precisely. As a methodology, it incorporates imprecision, subjective risk assessment, vague data information, and sensitivity analysis into the model formulation and solution process. In finance uncertainty is usually handled through the probability theory, which sometimes encounters difficulties. In general, probability calculus is not adapted to an imprecise corpus of knowledge, where as fuzzy calculus appears to be a more supple technique that provides pragmatic answers to problems under fuzzy environment. The use of fuzzy set theory, introduced by Zadeh [15] as a methodology for modeling and analyzing certain financial problems, is of particular interest to a number of researchers in option pricing ([1]−[3], [5], [7], [13]) due to fuzzy set theory’s ability to quantitatively and qualitatively model those problems which involve vagueness and imprecision. Option pricing theory can be traced back to Louis Bachelier [4]. Binomial option pricing [8, 10] is a simple but powerful technique that can be used to solve many complex option pricing problems. In the present paper we consider such a problem and on the lines of Muzzioli and Torricelli [13] and discuss the option pricing when payoffs are described by O(2, 2)-Tr.T.F.N. numbers. A numerical example is provided to illustrate the results.