不确定环境下的期权价格上下界研究

发布时间：2018-01-24 13:41

本文关键词： Knight不确定性期权价格上下界对偶规划风险中性定价　出处：《中国管理科学》2011年01期 　论文类型：期刊论文

【摘要】：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。
[Abstract]:The traditional option pricing theory is always based on the strict assumption of the underlying asset price distribution without considering the uncertainty of the distribution. This paper relaxes the strict assumption of the underlying asset price distribution. Under the condition of only knowing the first second moment and the first three moments of the asset price of the maturity date, and not knowing the specific distribution of the asset price, the option is priced. The information is insufficient and the distribution is uncertain. The derived option price is an interval. In view of the problem of solving the upper and lower bounds of option price under the condition of finite information, we establish a mathematical programming model. And it is transformed into a dual programming problem to be solved. The upper and lower bound and Black-Scholes price are compared and analyzed. The price of Black-Scholes is between the upper and lower bounds, relative to the upper and lower bounds derived by the first second moment. The upper and lower bounds derived from the first three moments information are narrower. In the time series analysis and cross section analysis using Hong Kong Hang Seng Index warrant data, it is found that the market price is indeed between the upper and lower bounds. The upper and lower bound ranges shrink with the decrease of volatility and residual duration. The pricing method in this paper does not need to make strict assumptions about asset price distribution, so it can improve the robustness of pricing model. It is helpful for investors to make investment decisions by combining the upper and lower limits of option prices and their subjective judgment.
【作者单位】：北京航空航天大学经济管理学院;
【基金】：国家自然科学基金(70671005,70821061)
【分类号】：F224;F830.9
【正文快照】： 1引言传统的资产定价理论,总是以“经济行为人能够对不确定自然状态做出确切概率估计”作为前提假定。事实上,面对充满了不确定因素的金融市场,这个假定是有局限性的。Keynes(1921)[1]对李嘉图后的主流经济学进行了根本性的批判,指出古典主义为了计算上的方便,为不确定性赋予

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