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Black-Scholes公式中无风险利率的常数假设与现实不符。本文假设无风险利率在一个区间中变动,讨论求期权价格区间问题。首先将此问题归结为一个随机最优控制问题,然后利用动态规划原理得到期权价格区间上下限满足的模型以及模型解法,并利用最优静态对冲缩小此价格区间,最后以BaiDu股票期权为例给出了模型在期权市场上的应用,提供了一种期权市场上的套利识别方法并与Black-Scholes公式的结果做了比较。
The constant assumption of the risk-free interest rate in the Black-Scholes formula does not correspond to reality. This paper assumes that the risk-free interest rate changes in a range and discusses the issue of asking price range. Firstly, the problem is reduced to a stochastic optimal control problem. Then the model of the upper and lower bounds of the option price range and the model solution are obtained by using the dynamic programming principle. The optimal static hedge is used to reduce the price range. Finally, BaiDu stock option is used as an example The application of the model to the option market provides a method of arbitrage recognition in the option market and compares it with the Black-Scholes formula.