Modeling Volatility of Daily Stock Return Using Generalized Autoregressive Conditional Heteroscadatic with Skewed Error Distribution and Stochastic Volatility Models

Abstract

The problem of how best to model volatility of stock prices returns have continued to occupy the minds of researchers in this area. This study therefore compares the performance of two competitive volatility models: The Stochastic Volatility (SV) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) based on skewed error distributions models using daily stock returns of Fourteen Nigerian banks. The daily stock closing price of the selected banks were collected for the period 4/1/2007 to 31/12/2021 and the stationarity, normality and ARCH effect of the series were tested. The parameter of SV and different types of GARCH models based on skewed normal, skewed student t and skewed generalized error distribution were estimated and selection of the best model was done using Akaike Information Criterion (AIC). Post estimation and evaluation were carried out using the Mean Square Error (MSE) and Root Mean Square Error (RMSE). Results of analysis revealed a stationary but asymmetrically distributed return series with ARCH effect. The model forecasting performance proved APARCH (1,1) based on student t-distribution as the best among the competing GARCH models with the record of the least AIC value in ten of the fourteen daily bank stocks returns. Although, APARCH (1,1) and SV models were found to be comparable. SV model was however recommended as the best since it recorded the least RMSE value in 11 (79%) of the 14 bank stocks against 3 (21%) bank stock in favour of APARCH (1,1). This implies that SV model was found to be adequate in modeling volatility of the daily stock returns of ECO Bank, First City Monument bank, Fidelity bank, first bank, Guaranty Trust bank, Stanbic IBTC bank, Sterling bank, United Bank for Africa, Union bank, WEMA bank and Zenith bank; while APARCH (1,1) base on Skewed student ‘t' distribution was preferred in modeling volatility of Access bank, Skye Bank and Unity bank. Results also showed the presence of volatility persistence, suggesting uncertainties and the risk of losses by investors. Therefore, it can be deduced that the application of a stochastic volatility model to the selected stock returns would drastically minimize the losses by investors.