We investigate Stochastic Processes that are mean reverting (and have leptokurtic distributions. A new MR process is proposed which utilizes the infinitely divisible property of Levy process. The process itself can be calibrated and simulated easily using a small number of discrete time steps. Further analysis is done on calculating the exponential compensator so that the log process can be simulated as a martingale. Results show that the model fits well to the empirical data and has the required properties.