A simple model for market booms and crashes

Multiple equilibria models are one of the major categories of theoretical models for stock market crashes. The main objective of this paper is to model multiple equilibria and demonstrate how market prices move from one regime into another in a continuous time framework. As a consequence of this, a multiple jump structure is obtained with both booms and crashes, which are defined as points of discontinuity of the stock price process. For the constructed model, we prove that the stock price is a càdlàg semimartingale process, find the conditional distributions for the time of the next jump, the type of the next jump and the size of the next jump, given the public information available to market participants, and conduct a number of numerical studies.