广东工业大学学报 ›› 2018, Vol. 35 ›› Issue (03): 87-89,112.doi: 10.12052/gdutxb.170175

• 综合研究 • 上一篇    下一篇

跳跃扩散下美式期权定价模型的高效算法

杨淑伶   

  1. 广东工业大学 应用数学学院, 广东 广州 510090
  • 收稿日期:2017-12-20 出版日期:2018-05-09 发布日期:2018-05-24
  • 作者简介:杨淑伶(1976-),女,讲师,硕士,主要研究方向为微分方程数值计算.E-mail:t_ysl@163.com
  • 基金资助:
     

An Efficient Algorithm for American Option Pricing in the Jump-Diffusion Model

Yang Shu-ling   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510090, China
  • Received:2017-12-20 Online:2018-05-09 Published:2018-05-24
  • Supported by:
     

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摘要： 研究跳跃扩散模型下美式期权定价问题的高效数值求解方法.首先在空间方向上利用高精度紧致差分格式离散期权定价模型，再对离散后所得到的常微分方程时间离散转化为线性互补问题.对线性互补问题的计算可求得期权价格的数值近似解.最后为了克服初始条件的不光滑性，对美式期权定价模型运用了奇异性分离的方法以提高计算结果的精度.数值实例验证了本文所建立算法的优越性.

关键词: 美式期权, 高精度紧致差分格式, 奇异性分离

Abstract: The efficient numerical methods for solving the American option pricing model under jump-diffusion is studied. First of all, the high accuracy compact difference scheme is applied to discrete the option pricing model in the spatial direction, and discrete the temporal variable of the resulting ordinary differential equation to the linear complementarity problem (LCP). The approximation value of option price is obtained by solving the LCP. Finally, in order to overcome the nonsmoothness of payoff function, the singularity separating method is utilized for the American option pricing model to improve the accuracy of calculation. Numerical examples demonstrate the superiority of the algorithm.

Key words: American option, high accuracy compact difference scheme, singularity separating method

中图分类号: 

  • O241.8
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