分数Black-Scholes模型下美式期权定价的积分方程式  

The Integral Equation Formula of American Option Pricing in the Fractional Black-Scholes Model

作　　者：林汉燕 袁媛 LIN Han-yan;YUAN Yuan(College of Science,Guilin University of Aerospace Technology,Guilin 541004,China)

机构地区：[1]桂林航天工业学院理学院,广西桂林541004

出　　处：《数学的实践与认识》2020年第12期293-298,共6页Mathematics in Practice and Theory

摘　　要：为得到分数Black-Scholes模型下美式期权价格的公式,文章以看涨期权为例,应用偏微分方程法,推导期权价格的积分方程式.由于美式期权的价格可分解为欧式期权的价格和由于提前实施需要增付的期权金,而提前实施期权金与最佳实施边界的位置有关,所以为导出最佳实施边界所满足的方程,文章首先研究分数Black-Scholes方程的基本解,然后建立美式看涨期权的分解公式,推导最佳实施边界适合的非线性积分方程,从而得到美式看涨期权价格的积分方程式.美式看跌期权价格的积分方程式类似得到.In order to get the formula of American option pricing in the fractional BlackScholes model,this paper takes the call option as an example,deduces a formula of integral equation of the option price by the partial differential equation.Due to the price of American options can be decomposed into European option price and the additional premium for early exercised,and the early exercised premium is related to the optimal exercise boundary.In order to derive the equations that the optimal exercise boundary satisfied,the basic solution of fractional Black-Scholes equation is studied firstly,then establish the decomposition formula for American call options,finally deduces the nonlinear integral equation of the optimal exercise boundary and get the integral equation formula of the price of American call option.The integral equation formula of the price of American put option is obtained similarly.

关 键 词：分数Black-Scholes模型 美式期权定价 非线性积分方程 

分 类 号：F224[经济管理—国民经济] F830.9