Options pricing in jump diffusion markets during financial crisis

In this paper, we suggest a jump diffusion model in markets during financial crisis. Using risk-neutral pricing, we derive a partial differential equation (P.D.E.) for the prices of European options. We find a closed form solution of the P.D.E. in the particular case where the stock price is too large. Then, we use such a solution as a boundary condition in the numerical treatment of the P.D.E. for any range of stock price. The numerical method adopted is the unconditionally stable Crank-Nicolson method. Illustrative examples are presented.