Financial options pricing with regime-switching jump-diffusions

We present a numerical method to evaluate financial derivatives under regime-switching jump-diffusion models. The prices of European and American options are derived by solving a partial integro-differential equation (PIDE) and a linear complementarity problem (LCP) respectively. We use the implicit method with three time levels to solve the PIDE and apply it coupled with the operator splitting method to solve the LCP. The proposed method has the advantage not only to avoid any fixed point iteration techniques at each time step, but also to evaluate directly the prices of the European and American options at all states of the economy. It is proved that the implicit method to solve the PIDE for the European option problem is stable with the second-order accuracy in the discrete ℓ2ℓ2-norm. We perform some numerical simulations to illustrate the analysis of the proposed method under the regime-switching jump-diffusion models.