Notice of Retraction

The main purpose of this paper is to study the stock price jump process is more common than Poisson process -a kind of special renewal process-the incident time interval is independent random variable sequence and identical subordinate to Gamma distribution. The object of study is European bi-direction option, It also known as the double two-way options. Also, European bi-direction option is an exotic option. Then, build up stochastic differential equation under the circumstance of the market no arbitrage based on stochastic analysis and martingale theory. Based on the above discussion, we obtain the European bi-direction option pricing formulas under jump diffusion model by simple mathematical induce by means of martingale method.