American Put-call Symmtry in Jump Diffusion Model

We derived symmetry relationships between the values and the optimal exercise boundaries of American puts and calls in a jump-diffusion model by the analytic method.Symmetry relationships between American calls and puts were obtained by probability theory.We gave here another proof of these results in the jump-diffusion model.Also,we showed some properties of American calls and American perpetual options in the jump-diffusion model by PDE arguments and our results.