A model of asset price dynamics is derived in which large jumps in sto
ck prices are determined endogenously. An important property of the mo
del is that it can lead to asset price distributions that are multimod
al. The model can explain how relatively small changes in dividends ca
n 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 framew
ork 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 ag
gregate stock price.