Modeling Time Varying Volatility and Asymmetry of Karachi Stock Exchange (KSE)

Abstract

Extensive work has been done on the modeling of financial time series, both theoretically and empirically, on developed markets of Europe, Asia and United states. There exist sufficient literature on volatility modeling of emerging markets as well, such as, of Latin America, Eastern and Central Europe and Asia. However due to inappropriate flow of information before the concept of so called Globalization many rapidly growing emerging markets could not attract the attention of financial researchers, such as, Karachi Stock Exchange (KSE) Pakistan, despite the fact that Bloomberg ranks the KSE-100, the benchmark Pakistani index, as the world's top-performing stock market in 2002 when Around the world, equity markets were grappling with tough times. This study can be considered as one of the very few attempts to model the most prominent features of the time series of KSE such as volatility clustering, excess kurtosis, and fat-tailedness by applying the most popular techniques proposed by Engle (1982), the Auto regressive Conditional Heteroscedasticity process (ARCH) and Bollerslev (1986), the Generalized Auto regressive Conditional Heteroscedasticity process (GARCH). Since, the intrinsically symmetric GARCH model does not cope with the asymmetry issues or so called effect, the Exponential Generalized Auto regressive Conditional Heteroscedasticity process (EGARCH) proposed by Nelson (1990) is used. Careful empirics lead us to report that in KSE-100 positive returns are associated with higher volatility than negative returns of equal magnitude and it is evident that past residuals highly influence current volatility. GARCH (1,1) is found to be best to capture the persistence in volatility while EGARCH (1,1) successfully overcome the so called leverage effect in KSE-100.