Option pricing by the martingale measure method considering the price of stock dividends payment and a jump-diffusion process

In this paper,it is assumed that the jump process in pricing of the underlying assets stock is a kind of special renewal process which is more common than the Poisson process considering the price of stock dividends payment.The stochastic differential equation is given in the case that the market has no arbitrage.Based on stochastic analysis and the martingale theory,the European call option pricing equation and the call-put parity formula are deduced under the contingent claim by means of the martingale measure pricing method.