不确定环境下的期权价格上下界研究

传统的期权定价理论总是建立在标的资产价格分布的严格假设下,而没有考虑分布的不确定性。本文对标的资产价格分布的严格假设进行放松,分别在仅知到期日标的资产价格的前二阶矩及前三阶矩,而不知道其具体分布的条件下,对期权进行定价。由于信息不充分及分布不确定,推导出的期权价格为一个区间。我们针对有限信息条件下求解期权价格上下界的问题,建立数学规划模型,并将其转化为对偶规划问题进行求解。对此上下界和Black-Scholes价格进行对比分析后发现,Black-Scholes价格介于此上下界之间,相对于采用前二阶矩推导的上下界,采用前三阶矩信息推导的上下界更窄。在使用香港恒生指数权证数据进行的时序分析及横截面分析中发现,市场价格确实介于上下界之间,上下界区间随波动率及剩余存续期的减小而缩小。采用本文的定价方法,不需要对资产价格分布进行严格假设,故可提高定价模型的稳健性,有助于投资者结合期权价格上下界及自己的主观判断进行投资决策。

Upper and Lower Bounds on Option Prices under Uncertainty

Traditional option pricing theories were based on the strict assumptions about underlying asset price process, which did not take Knightian uncertainty into consideration.In this article, those strict assumptions are relaxed and options are priced with only up to third order moment information.Due to limited information and the uncertainty of underlying price distribution, the option price can not be priced accurately.To derive upper and lower bounds for option prices with limited information, we build a programming model and solve the dual problem of this model.A comparative analysis between price bounds and Black-Scholes price is done afterwards.The bounds interval with up to third order moment information is narrower than those with only first and second order moment information.In the empirical research of Hong Kong's Hang Seng Index warrants, we find that the market prices indeed lie within the bounds.When volatility and remaining duration is small, upper and lower bounds interval is quite narrow.With this method, we can enhance the robustness of option pricing model, and help investors make investment decisions combining option price bounds and their subjective judgments.