跳跃扩散下美式期权定价模型的高效算法

杨淑伶

doi:10.12052/gdutxb.170175

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跳跃扩散下美式期权定价模型的高效算法

综合研究 | 更新时间：2026-05-27

- 跳跃扩散下美式期权定价模型的高效算法
- An Efficient Algorithm for American Option Pricing in the Jump-Diffusion Model
- 广东工业大学学报 2018年35卷第3期页码：87-89
- 作者机构：
  
  广东工业大学　应用数学学院,广东,广州,510090
- 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
- 基金信息：
- DOI：10.12052/gdutxb.170175
  中图分类号： O241.8
- 网络首发：2018-05-09，
  
  纸质出版：2018
- 稿件说明：
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杨淑伶. 跳跃扩散下美式期权定价模型的高效算法[J]. 广东工业大学学报, 2018, 35(3): 87-89.

Yang Shu-ling. An Efficient Algorithm for American Option Pricing in the Jump-Diffusion Model[J]. 2018, 35(3): 87-89.
杨淑伶. 跳跃扩散下美式期权定价模型的高效算法[J]. 广东工业大学学报, 2018, 35(3): 87-89. DOI： 10.12052/gdutxb.170175.

Yang Shu-ling. An Efficient Algorithm for American Option Pricing in the Jump-Diffusion Model[J]. 2018, 35(3): 87-89. DOI： 10.12052/gdutxb.170175.

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.

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.

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references

BLACK F, SCHOLES M. The pricing of options and corporate liabilities [J]. Journal of Political Economy, 1973, 81: 637-659.

MERTON R. Option pricing when underlying stock returns are discontinuous [J]. Journal of Finance Economics, 1976, 3: 125-144.

KOU S G. A jump-diffusion model for option pricing [J]. Management Science, 2002, 48(8): 1086-1101.

LIANG J. On the convergence rate of the binomial tree scheme for an American option with jump-diffusion [J]. Numerical Mathematics A Journal of Chinese Universities, 2008, 30(1): 76-96.

HE Y Y. A trinomial tree methods for princing American options [J]. Journal of Natural Science of Heilongjiang University, 2008, 25(1): 81-84.

ALMENDRAL A, OOSTERLEE C. Numerical valuation of options with jumps in the underlying [J]. Applied Numerical Mathematics, 2005, 53(1): 1-18.

HALLUIN Y, FORSYTH P, VETZAL K. Robust numerical methods for contingent claims under jump diffusion processes [J]. IMA Journal of Numerical Analysis, 2005, 25: 87-112.

FENG L, LINETSKY V. Pricing options in jump-diffusion models: an extrapolation approach [J]. Journal of the Operations Research Society of America, 2008, 56(2): 304-325.

ZHONG J M, CHAI Y Z, KONG F B, et al . Finite difference direct method for American put option [J ] . Journal of Chongqing Universityof Technology, 2011, 25(11): 106-110.

WANG L P, XU Z L, MA Q H, et al . Two kinds of finite difference scheme of pricing for American put options [J ] . Mathematics in Practice and Theory, 2012, 42(24): 33-38.

YANG S L, LEE S T, SUN H W. Boundary value methods with the Crank–Nicolson preconditioner for pricing options in the jump-diffusion model [J]. International Journal of Computer Mathematics, 2011, 88(8): 1730-1748.

SPOTZ W F, CAREY G F. Extension of high-order compact schemes to time-dependent problems [J]. Numerical Methods for Partial Ditierential Equations, 2001, 17(6): 657-672.

COTTLE R W, PANG J S, STONE R E. The linear complementarity problem[M]. London: Academic Press, 1992.

IKONEN S, TOIVANEN J. Operator splitting methods for American option pricing [J]. Applied Mathematics Letters, 2004, 17(7): 809-814.

ZHU Y L, WU X, CHERN I L. Derivatives securities and difference methods[M]. New York: Springer, 2004.

WANG J H, DONG Z H. Application of singularity-separating method in pricing American option [J]. Journal of Wuhan University Oftechnology, 2010, 32(5): 803-814.

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