Modeling Stock Market Monthly Returns Volatility Using GARCH Models Under Different Distributions

Rama Krishna Yelamanchili

doi:10.46281/ijafr.v5i1.425

Abstract

This papers aims to uncover stylized facts of monthly stock market returns and identify adequate GARCH model with appropriate distribution density that captures conditional variance in monthly stock market returns. We obtain monthly close values of Bombay Stock Exchange’s (BSE) Sensex over the period January 1991 to December 2019 (348 monthly observations). To model the conditional variance, volatility clustering, asymmetry, and leverage effect we apply four conventional GARCH models under three different distribution densities. We use two information criterions to choose best fit model. Results reveal positive Skewness, weaker excess kurtosis, no autocorrelations in relative returns and log returns. On the other side presence of autocorrelation in squared log returns indicates volatility clustering. All the four GARCH models have better information criterion values under Gaussian distribution compared to t-distribution and Generalized Error Distribution. Furthermore, results indicate that conventional GARCH model is adequate to measure the conditional volatility. GJR-GARCH model under Gaussian distribution exhibit leverage effect but statistically not significant at any standard significance levels. Other asymmetric models do not exhibit leverage effect. Among the 12 models modeled in present paper, GARCH model has superior information criterion values, log likelihood value, and lowest standard error values for all the coefficients in the model. 

Highlights

The key characteristics usually we find in asset returns are, high kurtosis, high Skewness, volatility clustering, asymmetry, and leverage effect
The conventional Generalized Autoregressive Conditional Heteroscedastic (GARCH) model has better information criterion values than asymmetric models suggesting that traditional GARCH model is adequate to capture conditional volatility of Sensex monthly returns series
In the squared log returns plots the return series has slow decay and there is a presence of significant autocorrelations and partial autocorrelations, suggesting that GARCH models may be appropriate to model the conditional volatility of Sensex monthly returns series

Summary

Introduction

The key characteristics usually we find in asset returns are, high kurtosis, high Skewness, volatility clustering, asymmetry, and leverage effect. (Mittal et al, 2012) report negative Skewness, high kurtosis, fat-tailed non-normal distribution, high persistence in volatility, presence of leverage effect. They suggest GARCH model for symmetric effects and PARCH model for asymmetric effects. In another context (Joshi, 2014) using three different models over the period 2010-2014 analyze Sensex and report mean reverting behavior, volatility clustering, persistence, and presence of leverage effect. We build symmetric and asymmetric GARCH models under different distributions. The conventional GARCH model has better information criterion values than asymmetric models suggesting that traditional GARCH model is adequate to capture conditional volatility of Sensex monthly returns series.

Data and Methodology

Findings

Conclusion