基于模糊二叉树模型的美式看跌期权定价问题

市场中影响期权价格的因素具有随机性和模糊性的特点。本文假定股票的价格波动为抛物型模糊数，推导出了模糊风险中性概率，进而将美式期权定价的传统二叉树模型扩展到模糊二叉树模型，给出了该模型的美式看跌期权定价过程和最优实施时间。最后的数值算例将该模型应用到国内的权证市场，针对唯一一只美式认沽权证进行定价分析，结果表明利用模糊二叉树模型定价能够得到一个合理的期权模糊价格区间。投资者可根据自身风险偏好程度改变置信水平和抛物型模糊数来进行投资决策。

Pricing of American put options based on a fuzzy binomial model

Both randomness and fuzziness should be considered when there is uncertainty in the market.In this paper the volatility of stock price was replaced by parabolic type fuzzy numbers.The fuzzy risk-neutral probabilities were then deduced in order to make a fuzzy binomial model,which is based on the binomial model.The price-setting process of American put options and the optimal exercise times were studied in detail.Furthermore,a numerical example was used to illustrate how to price a single put warrant in the Chinese domestic market.The results indicate that a rational fuzzy option price interval can be evaluated by a fuzzy binomial model and investors can make strategic decisions by changing the confidence levels and parabolic type fuzzy numbers.