Model construction of option pricing based on fuzzy theory

Abstract

Option pricing is a tool that investors often use for the purpose of arbitrage or hedging. However, both the Black-Scholes model and the CRR model can only provide a theoretical reference value. The volatility in the CRR model cannot always appear in the precise sense because the financial markets fluctuate from time to time. Hence, the fuzzy volatility is naturally to be considered. The main purpose of this paper is the application of fuzzy sets theory to the CRR model. It is expected that fuzzy volatility, instead of the crisp values conventionally used in the CRR model, can provide reasonable ranges and corresponding memberships for option prices, as a result of which, investors can interpret optimal value differently for different risk preferences. This paper shows a new method for option valuation using fuzzy set theory that is based on findings from earlier option valuation methods and from fuzzy membership function. In conclusion, the empirical evidence indicates the effectiveness of the proposed fuzzy model.