A model of asset price dynamics is derived in which large jumps instock prices are determined endogenously. An important property ofthe model is that it can lead to asset price distributions that aremultimodal. The model can explain how relatively small changes individends can lead to relatively large changes in asset prices and it can be used to identify the time period in which bubbles begin andend. The framework is applied to modeling the U.S. stock market crashin October 1987. Some forecasting experiments also are conducted withthe result that the model is able to predict the size of the eventualcrash in the aggregate stock price.