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