Abstract: We assumed that the stock price obeyed the CEV jump-diffusion model. Firstly, we gave the probability density function of the stock price by using It formula and Feller lemma of jump process. Secondly, we established the risk neutral measure by using the measure conversion of the compound Poisson process. Finally, under the condition of  the risk neutral measure, we gave the pricing formula of the European call option by using the riskfree discount of expected return.

Key words: CEV model, jumpdiffusion model, probability density , function, risk neutral pricing