支付红利下期权定价模型的一类高精度并行差分方法

全部作者: 赵卫娟,杨晓忠,吴立飞
作者单位: 华北电力大学数理学院信息与计算研究所
摘 要: 给出支付红利下期权定价模型的交替三点组显式(alternating three points group explicit,AGE-3)差分方法。在改进的Saul’yev不对称差分格式基础上,增加一个隐式点,构造了模型的三点组显式(three points group explicit,GE-3)差分格式,进而构造出AGE-3差分格式。理论分析和数值试验表明,模型的AGE-3差分方法是绝对稳定的,且数值解比交替分组显式(alternating group explicit, AGE)的解更加精确。数值试验还显示AGE-3格式的计算速度与AGE格式接近,约为改进的Saul’yev不对称格式计算时间的1/2,证实了该AGE-3差分格式并行计算方法的有效性和实用性。
关 键 词: 金融数学;支付红利下期权定价模型;交替三点组显式格式;并行计算;数值试验
Title: A kind of parallel difference method with high precision for the payment of dividend option pricing model
Author: ZHAO Weijuan, YANG Xiaozhong, WU Lifei
Organization: Institute of Information and Computation, Mathematics and Physics Department, North China Electric Power University
Abstract: This paper is given the alternating three points group explicit (AGE-3) difference method for the payment of dividend option pricing model. On the basis of the improved Saul’yev asymmetric difference scheme, three points group explicit (GE-3) difference scheme for the model is constructed increasing with an implicit point, then constructs the AGE-3 difference method for the model. Theoretical analysis and numerical experiment demonstrate that AGE-3 difference method of the model is unconditional stable and the calculation results more precise than solution of the alternating group explicit (AGE). Numerical experiment also shows that the computing speed of AGE-3 scheme is close to AGE scheme, about 1/2 times faster than the improved Saul’yev asymmetric difference scheme, which confirms the parallel computation method of AGE-3 difference scheme given by this paper is effective and practical.
Key words: financial mathematics; payment of dividend option pricing model; alternating three points group explicit scheme; parallel computing; numerical experiment
发表期数: 2016年4月第7期
引用格式: 赵卫娟,杨晓忠,吴立飞. 支付红利下期权定价模型的一类高精度并行差分方法[J]. 中国科技论文在线精品论文,2016,9(7):662-675.
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