A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model

Abstract EN

We present a stable finite difference scheme on apiecewise uniform mesh along with a penalty method for pricing Americanput options under Kou's jump-diffusion model.

By adding a penalty term,the partial integrodifferential complementarity problem arising from pricingAmerican put options under Kou's jump-diffusion model is transformed intoa nonlinear parabolic integro-differential equation.

Then a finite differencescheme is proposed to solve the penalized integrodifferential equation, whichcombines a central difference scheme on a piecewise uniform mesh with respectto the spatial variable with an implicit-explicit time stepping technique.

Thisleads to the solution of problems with a tridiagonal M-matrix.

It is provedthat the difference scheme satisfies the early exercise constraint.

Furthermore,it is proved that the scheme is oscillation-free and is second-order convergentwith respect to the spatial variable.

The numerical results support the theoreticalresults.