The Valuation of American Put Option Based on Fuzzy Techniques

Riskless interest rate and volatility are two important variables in option pricing model, but are hard to be estimated precisely. The concept of fuzziness is used to describe these variables in this paper. We apply fuzzy set theory to the American put option valuation and extend the fuzzy option pricing model by introducing riskless interest rate and volatility as two trapezoidal fuzzy numbers. The risk neutral probabilities are obtained as fuzzy numbers. Under fuzzy probabilities, we perform the risk neutral valuation of the American put option in a multi period binomial model. The price of the option at each step is expressed by a trapezoidal fuzzy number. Applying the binomial option pricing model, we illustrate a numerical example how to valuate the American put option based on fuzzy techniques. With a confidence level, the financial investors can shrink the option price interval and make the invest decision.