Modelling volatility in stock exchange data : a case study of three Johannesburg Stock Exchange (JSE) companies.

Abstract

For investors and policy makers such as governments, the uncertainty of returns on investments is a major problem. The aim of this paper is to study volatility models for financial data for both univariate and multivariate case. The data to be used is monthly and daily asset returns of three different companies. For the univariate case, the main focus is on GARCH models and their subsequent derivatives. ARCH and GARCH models of different orders are fit. For the monthly data, the GARCH(1,1)outperformed the ARCH and higher order GARCH models. For the daily data, the GARCH(1,1) preceded by an appropriate AR model was the best fit. For the Multivariate volatility models, models such as the DCC-GARCH, EMWA and Go-GARCH were used. All three gave similar results. Various distributional assumptions such as the normal and Student t distributions were assumed for the innovations. Student t and Skewed Student t distributions were more effective because of their ability to capture fat tails of the distributions. Fundamental finance terms and concepts are also discussed.