Modelling Stochastic Volatility of The Stock Market: A Nigerian Experience

In this paper, The GARCH (1,1)  model is presented and some results for the existence and uniqueness outlined. Other extensions of the GARCH model including EGARCH, PARCH and TARCH models were presented. The daily stock price of Dangote Cement (Dangocem) was used to test the performance of the above named models with respect to some stylized facts of volatility of financial data: fat tail, volatility clustering, volatility persistence, mean reversion and leverage effect. The Akaike Information Criterion (AIC), Schwarz Information Criterion (SIC) and the Hannan-Quinn criterion (HQ) were used to rate the performance of the models. The results show that the return series are stationary. The summary statistics showed that the return series has a fat tail. From the Q-Q plot, it was seen that the assumption of normality was spurious. The parameter estimation result showed that the volatility of the return series has the mean reversion property.. News impact was asymmetric and there is the presence of leverage effect. It was also seen that the volatility process was driven more by negative innovation. Overall the GARCH(1,1) and the TARCH model outperform the other model