SECOND-ORDER FINITE DIFFERENCE METHOD FOR OPTION PRICING UNDER JUMP-DIFFUSION MODELS

被引：73

作者：

Kwon, Yonghoon ^{[1
]}

Lee, Younhee ^{[2
]}

机构：

[1] Pohang Univ Sci & Technol, Dept Math, Pohang 790784, South Korea

[2] Pohang Univ Sci & Technol, Div Mech Engn Emerging Technol, Pohang 790784, South Korea

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2011年 / 49卷 / 06期

基金：

新加坡国家研究基金会;

关键词：

option pricing; finite difference method; partial integro-differential equation; Levy process; jump-diffusion model; EXPONENTIAL LEVY MODELS; RETURNS;

D O I：

10.1137/090777529

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a finite difference method to solve partial integro-differential equations which describe the behavior of option prices under jump-diffusion models. With localization to a bounded domain of the spatial variable, these equations are discretized on uniform grid points over a finite domain of time and spatial variables. The proposed method is based on three time levels and leads to linear systems with tridiagonal matrices. In this paper the stability of the proposed method and the second-order convergence rate with respect to a discrete l(2)-norm are proved. Numerical results obtained with European put options under the Merton and Kou models show the behaviors of the stability and the second-order convergence rate.

引用

页码：2598 / 2617

页数：20

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