An important aspect of the stock price process, which has of ten been ignored in the nancial literature, is that prices on organized exchanges are restricted to a grid. We consider continuous-time models for the stock price process with random waiting times of jumps and discrete jump size. We consider a class of jump processes that are close “to the Black-Scholes model in the sense that as the jump size goes to zero, the jump model converges to geometric Brownianmotion.