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中文摘要：
在市场含有Knight不确定因素的环境下，影响期权价格的因素不仅仅具有随机性的特点，而且还存在着模糊的性质。因而我们假设股票价格服从模糊随机过程，使用基于抛物型模糊数的二叉树模型对欧式期权进行定价，得到的风险中性概率及期权价格为一个赋权区间。在使用中国权证数据进行的实证中，采用二次规划方法确定模型参数，并对模糊期权价格进行去模糊化，与传统的二叉树模型进行实证比较后发现，应用模糊二叉树模型能得出更准确的市场价格预测。投资者可以选择自己可接受的置信度，得到一个模糊价格区间，以此指导投资策略。此外，应用此模型能够得到期权价格的模糊程度的度量一模糊度，从而获知Knight不确定性的大小。
英文摘要：
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.
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