Critical Analysis Of American Option In Jump-Diffusion Model

The intent of this paper is to discuss the critical property of price and optimal exercise boundary of American option when the expiry date runs to infinite in a jump-diffusion model. Different with the traditional diffusion models, the jump-diffusion models can be used to account for large changes in market prices due to sudden exogenous events. So they may explain some systematic empirical biases with respect to the Black-Scholes model. American option pricing problem is a free boundary problem of a parabolic integro-differential equation in jump-diffusion model, and perpetual American option pricing problem is a free boundary problem of integro-differential equation. Using the critical theory of partial differential equation, we obtain the critical estimates of a free boundary problem of integro-differential equation in limitless region, furthermore we prove that the price and optimal exercise boundary of American option converge to the price and optimal exercise boundary of perpetual American option respectively when the expiry date runs to infinite. In addition, we present the corresponding error estimates and numerical example coincide with the theory result of this paper, where we calculate the price of American option and perpetual American option with the binomial tree method and iterative method respectively.