Black-Scholes公式中无风险利率常数假设的一种改进  

An Amendment to the Assumption of Constant Risk-Free Interest Rate in Black-Scholes Formula

作　　者：杜玉林[1] 

机构地区：[1]华东政法大学商学院,201620

出　　处：《上海经济研究》2012年第4期67-73,共7页Shanghai Journal of Economics

摘　　要：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 assumption of constant risk-free interest rate in Black-Scholes formula cannot be satisfied in market. In this paper , we find the option price interval assuming the risk-free lies within a given interval. First we transform this financia/ problem to a stochastic optimal control problem, then obtain options＂ maximum and minimum price models through dynamic programming principle. We then discuss how to solve the nonlinear PDE model and how to narrow the price interval through optima/static hedging. We conclude this paper by giving its applieations in U. S. A option market through BaiDu options,comparing with Black-scholes, and giving a method how to identify arbitrage opportunity in option markets.

关 键 词：Black—Scholes公式 无风险利率常数假设 随机最优控制 套利识别 

分 类 号：F830.9[经济管理—金融学]