A rapid development of mathematical models and methods addressing uncertainty are reported in the literature in the recent past. These theories either extend and complement probability theory by introducing more general structures or provide an alternative framework. These works enable addressing of subjective risk assessment, vague data information and sensitivity analysis in a more flexible way. Recently, there has been growing interest in using fuzzy supported finance modelling. The systematic risk Beta of an asset is important in a variety of contexts, ranging from asset pricing theory, to hedging using index derivatives. The stability of Beta has been a matter of intense debate among researchers for the last three decades. In the current paper, fuzzy algebra is used to price financial options. Due to fluctuation of the financial market, some parameters in the the classical Cox-Ross-Rubinstein (CRR) binomial risk neutral option pricing model may not always be evaluated precisely. The authors propose to consider a crisp risk free rate assisted by CAPM return in the fuzzy option pricing model. The model is geared towards a more natural and intuitive way to deal with fuzziness, uncertainty and arbitrariness. The classical option pricing of CRR becomes a special case of the proposed model and some other special cases are also highlighted. The superiority and validity of the proposed fuzzy supported option pricing model is illustrated through a numerical example.

Most decision-making problems are ill defined as their objectives and model parameters are not precisely known [19]. Historically, probability and fuzzy sets have been presented as distinct theoretical foundations for reasoning and decision-making in situations involving uncertainty. Yet, when one examines the underlying axioms of both probability and fuzzy set theories, the two theories differ by only one axiom in a total of sixteen axioms needed for a complete representation [10]. But due to the fact that the requirements of the data and the environment are very strict and that many real world problems are fuzzy by nature and not random, the probability applications have not been very satisfactory in a lot of cases. In most real situation, one is forced to take decision on the basis of ill-defined variables and imprecise data. We are addressing in this paper one such real world problem of option pricing.