双币种期权定价模型的一个新ADI并行差分方法

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双币种期权定价模型的一个新ADI并行差分方法杨晓忠, 张帆, 吴立飞华北电力大学数理学院, 北京 102206 A New ADI Parallel Difference Method for Quanto Options Pricing Model YANG Xiaozhong, ZHANG Fan, WU LifeiSchool of Mathematics and Physics, North China Electric Power University, Beijing small 102206, China

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摘要双币种期权是一种重要的金融衍生产品，其定价模型是一个含有混合导数项的二维Black-Scholes方程，研究它的数值解法有着非常重要的理论意义和实际价值.本文给出求解双币种期权定价模型的基于Craig-Sneyd分裂法的一个新ADI差分方法(C-S ADI)，该方法首先将二维Black-Scholes方程分裂为两个一维方程和一个含有混合导数的二维方程，然后分别对一维方程构造半隐式格式，对含混合导数的二维方程构造显式格式进行计算.C-S ADI差分方法具有以下优点：并行性，无条件稳定性，收敛性及空间二阶、时间一阶的计算精度.
理论分析与数值试验表明，相比于经典的Crank-Nicolson差分格式和已有的基于Douglas-Rachford分裂法的ADI差分格式(D-R ADI)，本文格式计算精度更高，并且由于其具有天然的并行特性，本文格式比串行的Crank-Nicolson格式节省了近1/5的计算时间，证实了该方法对求解双币种期权定价模型是有效的.

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收稿日期: 2015-04-03

PACS:

O246

基金资助:国家自然科学基金（11371135），中央高校基本科研业务费专项资金资助（13QN30，2014ZZD10）资助项目.

引用本文:

杨晓忠, 张帆, 吴立飞. 双币种期权定价模型的一个新ADI并行差分方法[J]. 应用数学学报, 2016, 39(3): 403-418. YANG Xiaozhong, ZHANG Fan, WU Lifei. A New ADI Parallel Difference Method for Quanto Options Pricing Model. Acta Mathematicae Applicatae Sinica, 2016, 39(3): 403-418.

链接本文:

http://123.57.41.99/jweb_yysxxb/CN/或 http://123.57.41.99/jweb_yysxxb/CN/Y2016/V39/I3/403

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