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非线性Leland方程几类并行差分方法的数值分析

发表时间：2016-10-15 浏览量：3375 下载量：894

全部作者：	赵卫娟，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：	非线性Leland模型（含有支付交易费用的Black-Scholes期权定价模型）在期权定价中占有重要地位，对其数值解法的研究具有重要的理论意义和实际价值。研究首先给出一类高精度并行差分方法，即改进的交替分段Crank-Nicolson（improved alternating segment Crank-Nicolson，IASC-N）方法，其次理论分析该类方法具有存在唯一解、无条件稳定、计算精度为二阶的特性，最后通过数值试验比较IASC-N方法、交替分段Crank-Nicolson（alternating segment Crank-Nicolson，ASC-N）方法、交替分段显-隐（alternating segment explicit-implicit，ASE-I）方法等几类高精度并行差分方法。数值试验表明，IASC-N方法的计算精度为二阶，计算效率比ASC-N高，ASE-I方法的计算效率较好。综合比较，本研究给出的IASC-N并行差分方法是求解非线性Leland模型的实用方法。
关键词：	计算数学；非线性Leland模型；改进的交替分段Crank-Nicolson方法；交替分段显-隐方法；并行计算；数值试验
Title：	Numerical analysis of several kinds of parallel difference methods for nonlinear Leland equation
Author：	ZHAO Weijuan, YANG Xiaozhong
Organization：	Institute of Information and Computation, Mathematical & Physical Science School, North China Electric Power University
Abstract：	The nonlinear Leland model (nonlinear Black-Scholes option pricing model with transaction costs) occupies an important position in the option pricing and the study of numerical methods is of very important theoretical and practical significance. In this paper, we proposed a kind of high precision parallel difference method which is the improved alternating segment Crank-Nicolson (IASC-N) method. Theoretical analysis demonstrated that IASC-N method has characteristics with unique solution, unconditional stable and second order calculation precision. Finally, through numerical experiment, we compared IASC-N method, alternating segment Crank-Nicolson (ASC-N) method, and alternating segment explicit-implicit (ASE-I) method. Numerical experiments show that the calculation precision of IASC-N method is the second order, the computing efficiency of IASC-N method is taller than ASC-N method, and the computing efficiency of ASE-I method is good. By comprehensively comparing, IASC-N parallel difference method given by this paper is the most practical for solving nonlinear Leland model.
Key words：	computational mathematics; nonlinear Leland model; improved alternating segment Crank-Nicolson method; alternating segment explicit-implicit method; parallel computing; numerical experiments
发表期数：	2016年10月第19期
引用格式：	赵卫娟，杨晓忠. 非线性Leland方程几类并行差分方法的数值分析[J]. 中国科技论文在线精品论文，2016，9（19）：1963-1972.