【作者】 陈怡；

【导师】 唐万生；

【作者基本信息】 天津大学 ， 系统工程， 2007， 硕士

【摘要】 在金融市场中,期权作为衍生产品中应用最广泛的品种之一,发挥了越来越重要的作用。二叉树期权定价模型,由于其简单直观的构造,应用相当广泛,已成为金融界期权定价的基本方法之一。在现实生活中,由于信息不对称等原因,人们对未来状况的估计总是带有不确定因素的,从而基于个人主观判断或个人风险偏好的决策制定、项目评估的结果就会存在差异。因此,本文将可信性理论应用于传统的二叉树模型,以股票为标的资产,将股票价格设为模糊变量建立了模糊二叉树模型,并将该模型分别应用于欧式期权和美式期权中进行定价计算。为消除结果中的模糊性,本文采取计算期权价值的期望值的方法,求出清晰解以便投资者进行决策。在单期情况下,可求出期权价值的期望值的数值解,并且近似画出期权价值的隶属函数的图形。多期情况下,可通过模糊模拟的方法计算期望值。最后,本文还将模糊二叉树模型应用于实物期权的投资,并用算例验证了本文方法的有效性。更多还原

【Abstract】 As a kind of widely applied financial derivatives, options are play more and more important role in the financial market. Binomial options pricing model which have simple structure is widely used in the financial market and become one of the basic options pricing methods.In real world the future state of a system might not be known completely due to lack of information. Therefore, decision making which based on individuals’ subjective perceptions or personality tendencies for judgment, evaluation and decisions are different in many areas. In this paper, credibility theory is applied to traditional binomial model, stock price is assumed as fuzzy variable, then the fuzzy binomial tree model can be built to price European options and American options. With the approach of eliminating the fuzziness in the result, the method of getting expected value is adopted to help investor make descion. In one period model, numberical result of expected value can be got and the membership function of option value is approximately given. Fuzzy simulation is available for multiperiod case.Finally, fuzzy binomial tree model is apply to price real options, an example is also given to prove the validity of result.更多还原