While the demand for options can arise from many sources, our focus on jumps stems from fundamental considerations regarding the nature of price pro- cesses in an arbitrage-free economy. Recently, Madan [19] has argued that all arbitrage-free continuous time price processes must be both semi-martingales and time-changed Brownian motion. Furthermore, it is argued that if the time change is not locally deterministic, then the resulting price process is discontinuous. If the price is modelled as a pure jump L´ evy process with infinity activity, then the need for a continuous martingale component is obviated, since there will be an infinite number of small jumps in any time interval
