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双币种期权定价模型的一种快速AOS差分解法

发表时间:2012-01-15  浏览量:1776  下载量:556
全部作者: 周杲昕,杨晓忠
作者单位: 华北电力大学数理学院
摘 要: 使用快速加性算子分裂(additive operator splitting,AOS)算法将二维Black-Scholes方程转化为等价的一维方程组,再分别对2个一维方程构造‘显-隐’、‘隐-显’格式。从理论上分析该格式的相容性、稳定性和收敛性,并证明其具有二阶精度。最后,通过数值算例证明该格式的有效性,进一步说明通过快速AOS降维的方法能有效地避免高维Black-Scholes方程的计算复杂性,并且能较大幅度地提高计算速度,此方法能较好地适用于实时性要求较高的多资产期权定价。
关 键 词: 金融数学;双币种期权定价;快速加性算子分裂算法;‘显-隐’格式;‘隐-显’格式
Title: Accelerated additive operator splitting difference algorithm for dual currency option pricing model
Author: ZHOU Gaoxin, YANG Xiaozhong
Organization: Department of Mathematics and Physics, North China Electric Power University
Abstract: This paper uses the accelerated additive operator splitting (AOS) algorithm to transform the two-dimensional Black-Scholes equation into two equivalent one-dimensional equations, and then construct the‘explicit-implicit’ and the ‘implicit-explicit’ schemes. These schemes are proved to be stable, compatible and convergent, and they have second-order accuracy. Finally, the numerical example shows the effectiveness of the accelerated AOS difference schemes, which further illustrates that the accelerated AOS algorithm effectively avoids the computational complexity of the high-dimensional Black-Scholes equation, dramatically improves the computational speed, and is applicable for multi-asset option pricing.
Key words: financial mathematics; dual currency option pricing; accelerated additive operator splitting algorithm; ‘explicit-implicit’ scheme; ‘implicit-explicit’ scheme
发表期数: 2012年1月第1期
引用格式: 周杲昕,杨晓忠. 双币种期权定价模型的一种快速AOS差分解法[J]. 中国科技论文在线精品论文,2012,5(1):25-31.
 
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