D4 Published development or research report or study
A High-order Front-tracking Finite Difference Method for Pricing American Options under Jump-Diffusion Models (2008)

Toivanen, J. (2008). A High-order Front-tracking Finite Difference Method for Pricing American Options under Jump-Diffusion Models. University of Jyväskylä. Reports of the Department of Mathematical Information Technology. Series B, Scientific computing, 18/2008.

JYU authors or editors

Publication details

All authors or editors: Toivanen, Jari

ISBN: 978-951-39-3348-7

Journal or series: Reports of the Department of Mathematical Information Technology. Series B, Scientific computing

ISSN: 1456-436X

Publication year: 2008

Number in series: 18/2008

Number of pages in the book: 17

Publisher: University of Jyväskylä

Place of Publication: Jyväskylä

Publication country: Finland

Publication language: English

Publication open access: Not open

Publication channel open access: 

Additional information: Julkaistu myös lehdessä Journal of Computational Finance vol.13, nr 3 (March 2010) pp. 61-79 DOI: 10.21314/JCF.2010.222

Abstract

A free boundary formulation is considered for the price of American options under jump-diffusion models with finite jump activity. On the free boundary a Cauchy boundary condition holds due to the smooth pasting principle. An implicit finite difference discretization is performed on time-dependent non-uniform grids. During time stepping solutions are interpolated from one grid to another using Lagrange interpolations. Finite difference stencils are also constructed using Lagrange interpolation polynomials based on either three or five grid points. With these choices second-order and fourth-order convergence with respect to the number of time and space steps can be expected. In numerical examples these convergence rates are observed under the Black-Scholes model and Kou's jump-diffusion model.

Free keywords: American option; jump-diffusion model; free boundary problem; front-tracking method; finite difference method; moving grid; Lagrange interpolation

Contributing organizations

Ministry reporting: Yes

Preliminary JUFO rating: Not rated