Option pricing model on dividend-paying securities

This paper discusses the problem of pricing on European options in jump-diffusion model by martingale method. We assuming jump process are more general then Poisson process a kind of nonexplosive counting process. We discusses arbitrage pricing within the option pricing model under the assumption that the stock upon which an option is written pays dividends during option's lifetime.. By changing 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 of European options with dividends are obtained by stochastic analysis method. The results of R.C.Merton are generalized.