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支付红利下Black-Scholes方程的纯显-隐交替并行数值方法

发表时间:2017-01-15  浏览量:3635  下载量:1273
全部作者: 闫瑞芳,孙淑珍,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: Black-Scholes(B-S)方程是期权定价理论的基石,其数值解法的研究对许多金融衍生品定价方法具有显著的促进作用,对支付红利的B-S方程提出一类具有并行本性的数值方法--交替分段纯显-隐(pure alternative segment explicit-implicit,PASE-I)和纯隐-显(pure alternative segment implicit-explicit,PASI-E)差分格式,给出并行差分格式解的存在唯一性、稳定性、收敛性分析,理论分析和数值试验表明:PASE-I格式和PASI-E格式具有明显的并行计算性质,格式无条件稳定且空间、时间均二阶收敛,其整体计算精度优于已有的交替分段显-隐(ASE-I)和隐-显(ASI-E)差分格式,本文格式的计算时间与经典的C-N格式相比减少89.93%,表明PASE-I和PASI-E格式的并行数值方法求解支付红利下B-S方程是高效实用的。
关 键 词: 计算数学;支付红利下Black-Scholes方程;交替分段纯显-隐差分格式;稳定性;并行计算;数值试验
Title: Pure alternative segment explicit-implicit parallel difference methods for the payment of dividend Black-Scholes equation
Author: YAN Ruifang, SUN Shuzhen, YANG Xiaozhong
Organization: Institute of Information and Computation, School of Mathematics and Physics, North China Electric Power University
Abstract: Black-Scholes (B-S) equation is the cornerstone of option pricing theory and the research of the numerical solution has a significant effect on the pricing methods of many financial derivatives. In this paper, a numerical method with parallelism which were the pure alternative segment explicit-implicit (PASE-I) and pure alternative segment implicit-explicit (PASI-E) difference schemes for the payment of dividend B-S equation was proposed. It gave the existence and uniqueness, the stability and the convergence of numerical solution. Theoretical analysis and numerical experiments showed that PASE-I scheme and PASI-E scheme had obvious parallel computing properties and they were unconditionally stable and second-order convergence in both space and time. Their overall accuracies were better than that of the existing alternative segment explicit-implicit (ASE-I) and alternative segment implicit-explicit (ASI-E) difference schemes. The calculation time of our schemes could save 89.93% for classical Crank-Nicolson (C-N) scheme. It showed that the parallel numerical methods of PASE-I and PASI-E schemes were efficient and practical for solving the payment of dividend B-S equation.
Key words: computational mathematics; payment of dividend Black-Scholes equation; pure alternative segment explicit-implicit difference scheme; stability; parallel computing; numerical experiment
发表期数: 2017年1月第1期
引用格式: 闫瑞芳,孙淑珍,杨晓忠. 支付红利下Black-Scholes方程的纯显-隐交替并行数值方法[J]. 中国科技论文在线精品论文,2017,10(1):1-9.
 
13 评论数 2

用户2622648922:方法独特,计算格式具有显著的优势。

2017-03-29 14:11:24

用户Maggie:方法新颖 对我写论文有很大帮助

2017-03-29 14:07:46
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