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支付红利下Black-Scholes方程的一类并行差分数值方法

发表时间:2013-07-15  浏览量:1751  下载量:554
全部作者: 张帆,杨晓忠
作者单位: 华北电力大学数理学院信息与计算研究所
摘 要: 给出了支付红利下Black-Scholes方程具有近似二阶精度的改进Saul’yev不对称格式,在此基础上构造出方程的一类并行差分格式——交替分段显-隐(alternating segment explicit-implicit,ASE-I)格式和交替分段隐-显(alternating segment implicit-explicit,ASI-E)格式。理论分析表明该类格式是绝对稳定和收敛的,且具有明显的并行本性;数值试验表明此类格式较大幅度地提高了计算速度,其计算时间约为经典显-隐(隐-显)格式的1/2、Crank-Nicolson格式的1/5,并且其计算精度与显-隐(隐-显)格式精度接近,证实了该格式对求解支付红利下Black-Scholes方程的有效性。
关 键 词: 金融数学;支付红利下Black-Scholes方程;交替分段显-隐格式;并行算法;数值试验
Title: A parallel difference numerical method for solving the payment of dividend Black-Scholes equation
Author: ZHANG Fan, YANG Xiaozhong
Organization: Institute of Information and Computation, Mathematics and Physics Department, North China Electric Power University
Abstract: This paper constructed a new Saul’yev scheme with nearly second-order accuracy for solving the payment of dividend Black-Scholes equation, and then gave the alternating segment explicit-implicit (ASE-I) scheme and alternating segment implicit-explicit (ASI-E) scheme which were analyzed to be stable, convergent and parallel. The numerical examples showed that these two schemes could improve the calculation speed rapidly, and the calculation time of the two schemes was 1/2 of the ASE-I (ASI-E) scheme and 1/5 of the Crank--Nicolson scheme. The accuracy order of the two schemes was approximate to that of the explicit-implicit scheme, thus the schemes given by this paper could be used to solve the payment of dividend Black-Scholes equation effectively.
Key words: financial mathematics; payment of dividend Black-Scholes equation; alternating segment explicit-implicit scheme; parallel computing; numerical experiment
发表期数: 2013年7月第13期
引用格式: 张帆,杨晓忠. 支付红利下Black-Scholes方程的一类并行差分数值方法[J]. 中国科技论文在线精品论文,2013,6(13):1232-1241.
 
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