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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—模糊度,从而获知Knight不确定性的大小。
Under the circumstance that market contains uncertainty of Knight, the factors affecting the price of option are not only random but also fuzzy. Therefore, we assume that the stock price obeys the fuzzy stochastic process and uses the binary tree model based on the parabolic fuzzy number to price the European option. The obtained risk-neutral probability and the option price are a weighted interval. In the empirical study using Chinese warrants data, the quadratic programming method is used to determine the model parameters and the defuzzification of the price of the fuzzy options. Empirical comparison with the traditional binary tree model shows that using the fuzzy binary tree model can lead to more accurate Market price forecast. Investors can choose their own acceptable confidence, get a fuzzy price range, in order to guide investment strategy. In addition, the model can be used to measure the degree of ambiguity of the option price - the degree of ambiguity, so as to know the magnitude of Knight’s uncertainty.