A finite difference scheme for pricing american put options under kou's jump-diffusion model

We present a stable finite difference scheme on a piecewise uniform mesh along with a penalty method for pricing american put options under kou's jump-diffusion model. by adding a penalty term,the partial integrodifferential complementarity problem arising from pricing american put options under kou's jump-diffusion model is transformed into a nonlinear parabolic integro-differential equation. then a finite difference scheme is proposed to solve the penalized integrodifferential equation,which combines a central difference scheme on a piecewise uniform mesh with respect to the spatial variable with an implicit-explicit time stepping technique. this leads to the solution of problems with a tridiagonal m-matrix. it is proved that the difference scheme satisfies the early exercise constraint. furthermore,it is proved that the scheme is oscillation-free and is second-order convergent with respect to the spatial variable. the numerical results support the theoretical results. © 2013 jian huang et al.