模糊环境下美式看跌期权的定价研究

应用模糊集理论将无风险利率和波动率进行模糊化,以梯形模糊数替代精确值,将美式期权的定价模型扩展到美式期权模糊定价模型.得到了模糊风险中性概率表达式,并在此概率测度下推导出多期二叉树模糊定价模型,以及二叉树上各节点以梯形模糊数表示的模糊期权价值,以数值模拟演示了美式看跌期权的模糊定价过程.最后分析了不同风险偏好投资者在不确定环境下的套利决策行为,结果表明风险偏好大的投资者具有较高的置信水平、较小的主观模糊期权价格以及较大的无风险套利区间.

Pricing American Put Option under Fuzzy Environments

This paper adopted the fuzzy set theory to extend the pricing model of the American put option into the fuzzy option pricing model case by fuzzifying both riskless interest rate and volatility with the input parameters replaced by the trapezoidal fuzzy numbers.For this purpose,this paper first presented the expression of the fuzzy risk-neutral probabilities.Then the risk-neutral valuation of the American put option was performed in a multi-period binomial model,and the price of the option at each step was also expressed by a trapezoidal fuzzy number.Furthermore,a numerical example was illustrated how to price the American put option based on fuzzy techniques.Finally,the arbitrage decision behaviors of investors with different risk appetite were analyzed under uncertain environments.The results indicate that the investor with a high degree of risk appetite has a high confidence level,a wide interval for risk-less arbitrage but a small subjective fuzzy option price.