Journal of Computational Finance

A high-order front-tracking finite difference method for pricing American options under jump-diffusion models

Jari Toivanen


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 smoothpasting 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.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to View our subscription options

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here