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支付红利下期权定价模型分组显式差分的并行计算方法

发表时间:2015-07-15  浏览量:1735  下载量:905
全部作者: 郭瑶瑶,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: 支付红利下期权定价模型(Black-Scholes方程)数值解法的研究具有重要的理论和实际意义。给出支付红利下期权定价模型的分组显式(group explicit,GE)差分方法,在改进的Saul’yev不对称差分格式基础上,构造了支付红利下期权定价模型GE差分格式,进而构造出交替分组显式(alternating group explicit,AGE)差分格式。理论分析和数值试验表明,GE格式是条件稳定的,AGE格式是绝对稳定的。数值试验显示,AGE格式大幅度提高了计算速度,其计算时间约为改进的不对称差分格式的1/2,表明研究给出的AGE有限差分的并行计算方法对求解支付红利下期权定价模型有效。
关 键 词: 金融数学;支付红利下期权定价模型;分组显式差分格式;交替分组显式差分格式;并行计算;数值试验
Title: Parallel computation method of group explicit difference for the payment of dividend option pricing model
Author: GUO Yaoyao, YANG Xiaozhong
Organization: Institute of Information and Computation, Mathematics and Physics Department, North China Electric Power University
Abstract: It is very important to study the numerical solution for solving the payment of dividend option pricing model (Black-Scholes equation) both in theory and practice. This paper gives the group explicit (GE) difference method of the payment of dividend option pricing model. GE difference scheme is constructed based on the improved Saul’yev asymmetric difference scheme, then constructs the alternating group explicit (AGE) difference scheme. Theoretical analysis and numerical experiment demonstrate that GE scheme is conditional stable and AGE scheme is unconditional stable. The numerical experiment shows that AGE scheme can improve the calculation speed rapidly, the calculation time of AGE scheme is 1/2 of the improved Saul’yev asymmetric scheme, which confirms the parallel computation method of AGE finite difference given by this paper can be used to solve the payment of dividend option pricing model effectively.
Key words: financial mathematics; payment of dividend option pricing model; group explicit difference scheme; alternating group explicit difference scheme; parallel computing; numerical experiment
发表期数: 2015年7月第13期
引用格式: 郭瑶瑶,杨晓忠. 支付红利下期权定价模型分组显式差分的并行计算方法[J]. 中国科技论文在线精品论文,2015,8(13):1403-1416.
 
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