A Behavioral Model of Bubbles and Crashes

The aim of this paper is to provide one potential theoretical explanation for questions how asset bubbles come about, why it persists, and what caused it to burst. We propose a new model of bubbles and crashes. We divide the risky assets into two classes, the bubble asset and the non-bubble asset, and the risk-free asset. Investors are divided into two groups, the rational investors and the noise traders. The rational investors maximize their expected utility of their wealth in the next period. Noise traders maximize their random utility of binary choice: holding the bubble asset and holding the risk-free asst. We demonstrate that noise-traders’ herd behavior, which follows the behavior getting a majority, occurs when the number of noise-traders increases, and their herd behavior gives cause to a bubble, and their momentum trading prolongs bubble. However, rising stock price slows down as the noise-trader’s behavior approaches to a stationary state, so that the price momentum begins to decrease in the second half of bubble. We demonstrate that decreasing the price momentum lead to market crash