Abstract: Taking the Knightian uncertainty of financial market into consideration, the randomness and fuzziness of stock price should been evaluated by both probabilistic expectation and fuzzy expectation.We make use of parabolic type fuzzy numbers to discuss the fuzzy binomial option pricing model with uncertainty of both randomness and fuzziness, and derive expression for the fuzzy risk neutral probabilities, along with fuzzy expression for the fuzzy call prices As a consequence, we obtain weighted intervals for the risk neutral probabilities and for the expected fuzzy call price.The empirical research of an actual warrant from the China financial market shows that the fuzzy models presented in this paper could do better than the traditional binomial tree model in forecasting market price.This will allow a financial analyst to choose the European price at his acceptable degree of belief and make his investment strategies.

Key words: Knightian uncertainty, bino mial tree model, parabolic type fuzzy number, risk neutral pricing, defuzzification procedure, quadratic programming problem