Quantitative modelling of market booms and crashes

Multiple equilibria models are one of the main categories of theoretical models for stock market crashes. To the best of my knowledge, existing multiple equilibria models have been developed within a discrete time framework and only explain the intuition behind a single crash on the market. The main objective of this thesis 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 possible booms and crashes, which are defined as points of discontinuity of the stock price process. I consider five different models for stock market booms and crashes, and look at their pros and cons. For all of these models, I prove that the stock price is a cadlag semimartingale process and find 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. Finally, I discuss the problem of model parameter estimation and conduct a number of numerical studies.