To be consistent with the general efficient market hypothesis of Fama (1970) and Samuelson (1965b), the dynamics of the unanticipated part of the stock price motions should be a martingale. Just as once the dynamics are posited to be a continuous-time process, the natural prototype process for the continuous component of the stock price change is a Wiener process, so the prototype for the jump component is a ‘Poisson-driven’ process.