A Second-order Finite Difference Method for Option Pricing Under Jump-diffusion Models

Authors:
YongHoon Kwon;Younhee Lee
Affiliations:
ykwon@postech.ac.kr;lyounhee@postech.ac.kr
Venue:
SIAM Journal on Numerical Analysis
Year:
2011

Citing 5
Cited 1

A Jump-Diffusion Model for Option Pricing

Management Science
Convergence of numerical schemes for viscosity solutions to integro-differential degenerate parabolic problems arising in financial theory

Numerische Mathematik
Finite Differences And Partial Differential Equations

Finite Differences And Partial Differential Equations
A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models

SIAM Journal on Numerical Analysis
Numerical valuation of options with jumps in the underlying

Applied Numerical Mathematics

Tridiagonal implicit method to evaluate European and American options under infinite activity Lévy models

Journal of Computational and Applied Mathematics

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Abstract

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 $\ell^{2}$-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.