Wang, Xiaolei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 34-39). / Abstracts in English and Chinese. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Identification of Stock Market Crashes --- p.5 / Chapter 2.1 --- Identification Criteria --- p.7 / Chapter 2.2 --- Identification Results --- p.8 / Chapter Chapter 3. --- Data --- p.10 / Chapter 3.1 --- Data Issue for Chapter 4 --- p.10 / Chapter 3.2 --- Data Issue for Chapter 5 --- p.12 / Chapter 3.3 --- Data Issue for Chapter 6 --- p.12 / Chapter Chapter 4. --- Examination of AFE --- p.13 / Chapter 4.1 --- Definition of AFE and MAAFE --- p.13 / Chapter 4.2 --- Examination of MAAFE --- p.14 / Chapter 4.3 --- Examination of AFE by Grouping Duration --- p.15 / Chapter Chapter 5. --- Examination of AFD --- p.18 / Chapter Chapter 6. --- Examination of the Relationship between AFD and ESR --- p.22 / Chapter 6.1 --- Portfolio Strategy - Sorting by Size and Dispersion --- p.23 / Chapter 6.2 --- Portfolio Strategy - Sorting by Size and Book to Market Ratio --- p.26 / Chapter 6.3 --- Fama-French Time Series Regression Test (Three-Factor Model) --- p.28 / Chapter 6.4 --- Fama-French Time Series Regression Test (Three-Factor Model with Dispersion on the Right Hand Side) --- p.30 / Chapter 6.5 --- Introduction of a Nonlinear Form of AFD to the Fama-French Model --- p.31 / Chapter Chapter 7. --- Conclusions --- p.32 / References --- p.34 / Appendix Table I to Table XVI --- p.40-55 / Figure I to Figure VI --- p.56-61

Forecasting volatility with precision in financial market is very important. This paper examines the use of various forms of GARCH models for forecasting volatility. Three financial data sets from Japan (NIKKEI 225 index), the United States (Standard & Poor 500) and Germany (DAX index) are considered. A number of GARCH models, such as EGARCH, IGARCH, TGARCH, PGARCH and QGARCH models with normal distribution and student’s t distribution are used to fit the data sets and to forecast volatility. The Maximum Likelihood method and the Bayesian approach are used to estimate the parameters in the family of the GARCH models. The results show that the QGARCH model under student’s t distribution is the precise model for the NIKKEI 225 index in terms of fitting the data and forecasting volatility. The TGARCH under the student’s t distribution fits the S&P 500 index data better while the traditional GARCH model under the same distribution performs better in forecasting volatility. The PGARCH with student’s t distribution is the precise model for the DAX index in terms of fitting the data and forecasting volatility. / Department of Mathematical Sciences