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非线性Leland方程交替三点组显式差分的并行计算方法

发表时间:2017-04-14  浏览量:1348  下载量:192
全部作者: 傅宇明,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方程是考虑支付交易费用的非线性Black-Scholes(B-S)期权定价模型之一,对其数值方法的研究具有非常重要的理论意义和实际价值。针对Leland模型,构造一种具有并行本性的差分数值方法——交替三点组显式(alternating three points group explicit,AGE-3)方法,给出AGE-3格式的稳定性及解的误差估计。理论分析表明AGE-3格式是绝对稳定的,数值试验显示AGE-3格式较已有的隐式格式和交替分段Crank-Nicolson(alternating segment Crank-Nicolson,ASC-N)格式大幅度提高了计算速度,节省了99%的时间,表明AGE-3格式对求解非线性Leland方程是高效的。
关 键 词: 金融数学;非线性Leland模型;交替三点组显式方法;并行计算;数值试验
Title: Parallel computation method by alternating three points group explicit difference for nonlinear Leland equation
Author: FU Yuming, YANG Xiaozhong
Organization: Institute of Information and Computation, Mathematics and Physics Department, North China Electric Power University
Abstract: Nonlinear Leland equation is one of Black-Scholes (B-S) option pricing model with transaction costs. The study of the numerical method is of important theoretical significance and practical value. In view of Leland model, we constructed a kind of difference numerical method with intrinsic parallelism: alternating three points group explicit (AGE-3) method. Theoretical analysis demonstrates that AGE-3 difference method of the model is unconditionally stable. The stability of the AGE-3 scheme and the error estimate of the solution are given. The numerical experiment shows that AGE-3 scheme can improve the calculation speed rapidly in contrast with implicit scheme and alternating segment Crank Nicolson (ASC-N) scheme, where 99% time was saved, thus the AGE-3 method can be used to solve the nonlinear Leland equation effectively.
Key words: financial mathematics; nonlinear Leland equation; alternating three poiats explicit method; parallel computing; numerical experiments
发表期数: 2017年4月第7期
引用格式: 傅宇明,杨晓忠. 非线性Leland方程交替三点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,2017,10(7):718-732.
 
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