Pricing European options on dividend-paying stock

Abstract

In this paper, we study the problem of pricing on European options under the jump-diffusion model. Jump-diffusion asset price model is driven by nonexplosive counting process that is more general than Poisson process. We assume that the dividend is to be paid at a specified time,with the amount paid equal to a fixed fraction of the price of the security or to a fixed amount. With risk-neutral martingale measure, applying stochastic analysis methods, the behavior model of the stock pricing process is jump-diffusion process is established. Furthermore, we derive pricing formula of European option and put-call parity relation with dividends.