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时间-空间分数阶Black-Scholes方程的一类高效差分方法

发表时间:2018-10-15  浏览量:124  下载量:31
全部作者: 李玥,杨晓忠,孙淑珍
作者单位: 华北电力大学数理学院
摘 要: 分数阶Black-Scholes(B-S)方程的数值解法对金融衍生品定价研究发挥着显著的促进作用。针对时间-空间分数阶B-S方程构造出显-隐(explicit-implicit,E-I)差分格式和隐-显(implicit-explicit,I-E)差分格式,这类格式由古典显式格式和古典隐式格式相结合构造而成。理论分析证明了E-I和I-E格式解的存在唯一性、无条件稳定性和收敛性。数值试验证实E-I和I-E格式具有相同的计算复杂度,在计算精度相近的条件下,其计算时间比Crank-Nicolson(C-N)格式减少约33%,数值试验与理论分析结果一致。E-I和I-E差分方法对求解时间-空间分数阶B-S方程是高效可行的,同时也证明了分数阶B-S方程更符合实际金融市场。
关 键 词: 计算数学;时间-空间分数阶Black-Scholes(B-S)方程;显-隐差分格式和隐-显差分格式;稳定性;收敛性;数值试验
Title: A class of efficient difference methods for time-space fractional Black-Scholes equation
Author: LI Yue, YANG Xiaozhong, SUN Shuzhen
Organization: School of Mathematics and Physics, North China Electric Power University
Abstract: The numerical solutions of the fractional Black-Scholes (B-S) equation play a significant role in the pricing study of many financial derivatives. This paper proposes a class of explicit-implicit (E-I) and implicit-explicit (I-E) difference schemes for time-space fractional B-S equation. The E-I and I-E schemes are combined by classic explicit scheme and classic implicit scheme. And their solutions are proved to be existing and unique, unconditionally stable and convergent by theoretical analysis. The numerical experiments demonstrate that the two schemes have the same computational complexity. Under the similar calculation precision, they save about 33% of the computation time compared to Crank-Nicolson (C-N) scheme. The numerical experiments are consistent with the theoretical analysis. The E-I and I-E difference methods are efficient to solve the time-space fractional B-S equation and fractional B-S equation is more suitable for actual financial market.
Key words: computational mathematics; time-space fractional Black-Scholes (B-S) equation; explicit-implicit (E-I) and implicit-explicit (I-E) difference schemes; stability; convergence; numerical experiments
发表期数: 2018年10月第19期
引用格式: 李玥,杨晓忠,孙淑珍. 时间-空间分数阶Black-Scholes方程的一类高效差分方法[J]. 中国科技论文在线精品论文,2018,11(19):1902-1913.
 
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