| 有限体积法定价跳扩散期权模型 |
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| 引用本文： | 甘小艇,殷俊锋,李蕊. 有限体积法定价跳扩散期权模型[J]. 同济大学学报(自然科学版), 2016, 44(9): 1458-1465 |
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| 作者姓名： | 甘小艇 殷俊锋 李蕊 |
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| 作者单位： | 同济大学 数学系, 上海 200092；楚雄师范学院 数学与统计学院，云南 楚雄 675000,同济大学 数学系, 上海 200092,同济大学 数学系, 上海 200092；嘉兴学院 数理与信息工程学院, 浙江 嘉兴 314001 |
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| 基金项目： | 国家自然科学基金项目（填写项目编号）11271289,中央高校基本科研业务费专项资金, 云南省应用基础研究计划青年项目(2013FD045),云南省教育厅科学研究基金项目(2015Y443). |
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| 摘 要： | 考虑有限体积法求解Kou模型下美式跳扩散期权.基于线性有限元空间,构造了向后欧拉和Crank-Nicolson两种全离散有限体积格式,并采用简单高效的递推公式对偏微分积分方程中的积分项进行逼近.针对美式期权离散得到的线性互补问题(LCP),采用模超松弛迭代法(MSOR)进行求解,并证明了H_+离散矩阵下算法的收敛性.数值实验表明,所构造的方法是高效而稳健的.
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| 关 键 词： | 有限体积法 Kou跳扩散期权模型 线性互补问题 模超松弛迭代法 |
| 收稿时间： | 2015-11-09 |
| 修稿时间： | 2016-06-07 |
Finite Volume Methods for Pricing Jump Diffusion Option Model |
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| GAN Xiaoting,YIN Junfeng and LI Rui. Finite Volume Methods for Pricing Jump Diffusion Option Model[J]. Journal of Tongji University(Natural Science), 2016, 44(9): 1458-1465 |
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| Authors: | GAN Xiaoting YIN Junfeng LI Rui |
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| Affiliation: | Department of Mathematics, Tongji University, Shanghai 200092, China; School of Mathematics and Statistics, Chuxiong Normal University, Chuxiong Yunnan 675000, China,Department of Mathematics, Tongji University, Shanghai 200092, China and Department of Mathematics, Tongji University, Shanghai 200092, China; College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing Zhejiang 314001, China |
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| Abstract: | Finite volume methods are developed for pricing American options under Kou jump diffusion model. Based on a linear finite element space, both backward Euler and Crank Nicolson full discrete finite volume schemes are constructed. For the approximation of the integral term in the partial integro differential equation (PIDE), an easy to implement recursion formula is employed. Then we propose the modulus based successive overrelaxation (MSOR) method for the resulting linear complementarity problems (LCPs). The H+ matrix property of the system matrix which guarantees the convergence of the MSOR method is analyzed. Numerical experiments confirm the efficiency and robustness of the proposed methods. |
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| Keywords: | finite volume method Kou jump diffusion option model linear complementarity problem modulus based successive overrelaxation method |
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