Black-scholes期权定价公式的显式差分近似  

An Explicit Approximation for Black-scholes Option Pricing Formula

作　　者：梁娟 赵治荣 张园园 LIANG Juan;ZHAO Zhi-rong;ZHANG Yuan-yuan(Department of Science,Taiyuan Institute of Technology,Taiyuan Shanxi,030008;School of Resources and Environment,Shanxi University of Finance and Economics,Taiyuan Shanxi,030006)

机构地区：[1]太原工业学院理学系,山西太原030008 [2]山西财经大学资源环境学院,山西太原030006

出　　处：《山西大同大学学报（自然科学版）》2020年第5期46-49,共4页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：山西省自然科学基金项目[201901D111322]。

摘　　要：研究了期权价格变化的Black-scholes方程,利用Δ-对冲原理和Itô积分公式,通过函数变换转化为抛物线方程,并通过泰勒展开得到了方程的差分格式。证明了差分格式的相容性、差分解的稳定性以及敛散性.通过数值模拟,验证了差分格式的有效性。In this paper,the Black-scholes equation of option price change is studied.By using-hedge principle and integral for⁃mula,the function transformation is transformed into parabolic equation,and the difference scheme of the equation is obtained by Tay⁃lor expansion.The compatibility,stability,convergence and divergence of the difference scheme are proved.The validity of the differ⁃ence scheme is verified by numerical simulation.

关 键 词：BLACK-SCHOLES方程 有限差分格式 相容性 数值实验 

分 类 号：O242.21[理学—计算数学]