Option Pricing Model With Continuous Dividends

This paper discusses the problem of pricing on European options in jump-diffusion model by martingale method. We assuming jump process are more commen then Possion process a kind of nonexplosive counting process. Supposing that the dividend for each share of the security is paid continuously in time at a rate equal to a fixed fraction of the price of the security. By changing the basic assumption of R.C.Merton option pricing model to the assumption. It is established that the behavior model of the stock pricing process is jump-diffusion process. With risk-neutral martingale measure, pricing formula and put-call parity for European options with continuous dividends are obtained by stochastic analysis method. The results of Margrabe are generalized.