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时间分数阶Black-Scholes方程的θ-差分数值方法

发表时间:2014-07-15  浏览量:1963  下载量:849
全部作者: 张雪,孙淑珍,吴立飞,杨晓忠
作者单位: 华北电力大学数理学院
摘 要: 基于分数布朗运动驱动的分数阶随机微分方程描述股票价格变化更符合实际金融市场规律,研究分数阶Black-Scholes方程的数值解法具有非常重要的理论意义和实际应用价值。对时间分数阶Black-Scholes方程构造了θ-差分格式,分析此格式解的存在唯一性、稳定性和收敛性。并通过数值试验证实了θ-差分格式对求解时间分数阶Black-Scholes方程是有效的,且计算速度较快。
关 键 词: 金融数学;时间分数阶Black-Scholes方程;θ-差分格式;稳定性;数值试验
Title: θ-difference numerical method for solving time-fractional Black-Scholes equation
Author: ZHANG Xue, SUN Shuzhen, WU Lifei, YANG Xiaozhong
Organization: Mathematics and Physics School, North China Electric Power University
Abstract: It’s more practical and more actual in financial markets to use stochastic differential equation driven by fractional Brownian motion to describe the stock price. So it is very practical in the application to study the numerical computation of fractional Black-Scholes equation. This paper constructs θ-difference scheme for solving the time-fractional Black-Scholes equation. The θ-difference scheme is analyzed to be stable, convergent, existence and uniqueness of solution. Finally, this paper proves the effectiveness of θ-difference scheme for solving Black-Scholes by numerical experiments, and its calculating speed is faster.
Key words: financial mathematics; time-fractional Black-Scholes equation; θ-difference scheme; stability; numerical experiment
发表期数: 2014年7月第13期
引用格式: 张雪,孙淑珍,吴立飞,等. 时间分数阶Black-Scholes方程的θ-差分数值方法[J]. 中国科技论文在线精品论文,2014,7(13):1287-1295.
 
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