Three Essays on Financial Modelling with Price Limits

Abstract

In this thesis, a class of clustered censored distributions are proposed in various financial modelling processes. In particular, the proposed distribution can accommodate many stylized (observed) phenomena across different stock markets, especially those with price limits. One main attractive characteristics of the proposed distribution is that it can capture the clustered behaviour of the data over certain continuous interval (while the traditional censored distribution can only allow the clusters to be on the bounds). The clustered censored distribution is developed and presented, to some extent, in a general way so that it can be transformed into other well-known distributions, such as the classical Normal distribution, one- (or two-) sided truncated distribution, one- (or two-) sided censored distribution, etc. The clustered censored distribution is further designed into some well-known financial modelling structures, such as Generalized Autoregressive Conditional Heteroskedasticity (GARCH, Bollerslev (1986)) process. We also investigate the potential applications of the proposed models in this thesis to risk management. Overall, there are three main chapters in the thesis. Chapter 1 introduces the fundamental theory and properties of the proposed clustered censored distribution. As a starting point, Normality is mainly considered in this chapter. Built on Chapter 1, Chapter 2 designs a GARCH process with the cluster censored Normal distribution (referred as GARCHCCN). The model performance is investigated via Monte Carlo experiments and empirical data. The risk implication is also discussed in Chapter 2. Chapter 3 consists of two dimensions of the extensions. Sections 3.1-3.4 extend the model using clustered censored heavy tailed distributions, such as Student-t and Generalized Error Distribution (GED), for a better performance in capturing the tail behaviour. Section 3.5 examines the dynamic spillover effects under the proposed model framework. There are 14 supporting appendices (A-N) mainly for proofs, tables and figures.