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跳扩散过程下期权定价的数值方法

黎伟 周圣武

黎伟, 周圣武. 跳扩散过程下期权定价的数值方法[J]. 华东师范大学学报(自然科学版), 2012, (4): 27-35.
引用本文: 黎伟, 周圣武. 跳扩散过程下期权定价的数值方法[J]. 华东师范大学学报(自然科学版), 2012, (4): 27-35.
LI Wei, ZHOU Sheng-wu. Numerical method for option pricing under jump-diffusion process[J]. Journal of East China Normal University (Natural Sciences), 2012, (4): 27-35.
Citation: LI Wei, ZHOU Sheng-wu. Numerical method for option pricing under jump-diffusion process[J]. Journal of East China Normal University (Natural Sciences), 2012, (4): 27-35.

跳扩散过程下期权定价的数值方法

详细信息
  • 中图分类号: O211.6, F830.9

Numerical method for option pricing under jump-diffusion process

  • 摘要: 研究了跳扩散过程下期权价值所满足\,PIDE\,方程的数值计算方法. 利用四阶差分格式对空间离散, 引入四阶\,Lagrange\,插值多项式对边界进行延拓, 得到一个非齐次线性系统. 基于矩阵指数的\,$\mathrm{Pad\acute{e}}$\,逼近方法及其分数表示形式, 构建了一种高阶光滑\,Crank-Nicolson\,差分格式. 数值计算验证了该种方法的有效性, 讨论了跳跃强度对标准期权和障碍期权的影响. 与传统的\,Crank-Nicolson\,格式相比, 该格式很好地处理了在执行价格和障碍点附近数值震荡的问题. 该种方法亦可应用于一般具有非光滑边界的线性系统问题.
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出版历程
  • 收稿日期:  2011-09-01
  • 修回日期:  2012-01-01
  • 刊出日期:  2012-07-25

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