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总览 评价 闫瑞芳 ， 孙淑珍 * ， 杨晓忠 （ 华北电力大学数理学院信息与计算研究所，北京 102206； ） 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
闫瑞芳， 孙淑珍*， 杨晓忠
（
华北电力大学数理学院信息与计算研究所，北京 102206； ）
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：
支付红利下Black-Scholes（B-S）方程；交替分段纯显-隐（PASE-I）差分格式；稳定性；并行计算；数值试验
YAN Ruifang， SUN Shuzhen*， YANG Xiaozhong
（
Institute of Information and Computation, Mathematics and Physics School, North China Electric Power University, Beijing 102206, China； ）
Abstract：
Black-Scholes equation was the cornerstone of option pricing theory and the research of the numerical solution had a significant effect on the pricing methods of many financial derivatives. This paper proposed a numerical method with parallel class nature which were the pure alternative segment explicit-implicit (PASE-I) and implicit-explicit (PASI-E) difference scheme for the payment of dividend B-S equation. It gave the existence and uniqueness，the stability and the convergence of numerical solution. Theoretical analysis and numerical experiments showed that PASE-I format and PASI-E format had obvious parallel computing properties and they were unconditionally stable and second-order convergence in both space and time. Their overall accuracy was better than that of the existing alternating segment explicit-implicit (ASE-I) and the implicit-explicit (ASI-E) difference scheme. The calculation time of our schemes could saved 89.93% for classics Crank-Nicolson scheme. It showed that the explicit-implicit alternating parallel numerical method was efficient and practical for solving the payment of dividend B-S equation.
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