In this process, the bubble factor grows by the exact amount needed to compensate investors for the probability, 1-p , that the bubble will crash and revert to the small initial value, a0>0. 6 In order for the Blanchard and Watson model to be consistent with the two traditional characteristics of bubbles, a long run-up in price followed by a crash, the probability of the bubble continuing, p , must be greater than 1/2.