Kou跳扩散模型下美式期权定价的隐–显三阶SBDF法

doi:10.12677/AAM.2018.71014

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Kou跳扩散模型下美式期权定价的隐–显三阶SBDF法
IMEX Third-Order SBDF Scheme for Pricing American Options under Kou’s Jump-Diffusion Models

DOI: 10.12677/AAM.2018.71014, PDF, HTML, XML, 下载: 1,897 浏览: 2,568 国家自然科学基金支持
作者: 贾翔宇, 许作良：中国人民大学，信息学院，北京
关键词: 隐–显方法；线性多步法；跳扩散模型；期权定价；傅里叶稳定性分析；Implicit-Explicit Methods； Linear Multistep Methods； Jump-Diffusion Model； Option Pricing； Fourier Stability Analysis

摘要: 本文讨论跳扩散过程下期权定价模型的偏积分微分方程的隐–显三阶SBDF时间离散格式。我们引入参数c∈[0,1]，使由跳跃产生的零阶项变成一个关于c的凸组合，并将其分别加入到隐式部分和显式部分；并应用傅里叶分析研究该方法的稳定性。在适当的假设条件和时间步长限制下，我们证明了隐–显三阶SBDF方法对于所有的c∈[0,1]是条件稳定的。数值实验表明了该方法的有效性。

Abstract: We consider IMEX third-order SBDF time discretization scheme for the partial integro-differential equation derived for the pricing of options under a jump-diffusion process. The scheme is defined by a convex combination parameter c∈[0,1], which divides the zeroth-order term due to the jumps between the implicit and explicit parts in the time discretization. This scheme is studied through Fourier stability analysis. It is found that, under suitable assumptions and time step re-strictions, the IMEX third-order SBDF scheme is conditionally stable for all c∈[0,1]. Numerical experiments show the effectiveness of the proposed method.

文章引用：贾翔宇, 许作良. Kou跳扩散模型下美式期权定价的隐–显三阶SBDF法[J]. 应用数学进展, 2018, 7(1): 109-117. https://doi.org/10.12677/AAM.2018.71014

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