VOLATILITY FORECASTING IN INDIAN EQUITY MARKETS: A COMPARATIVE STUDY OF GARCH, EGARCH, GJR-GARCH, AND HESTON MODELS ON NIFTY 50

Abstract

Forecasting of volatility is fundamental to the modern financial econometrics literature. Its practical applications can be found in risk management, option pricing, and asset allocation. Although a large body of literature has concentrated on volatility modeling in developed countries’ stock markets, there are comparatively fewer empirical studies examining different volatility models in emerging markets such as the Indian stock market. In this paper, four volatility models — GARCH(1,1), EGARCH(1,1), GJR-GARCH(1,1), and the Heston Stochastic Volatility model — are applied to daily returns of the NIFTY 50 Index for the period January 2005 to March 2025. The dataset consists of 4,999 daily trading observations. This study adopts a two-stage methodology to conduct the empiri cal analysis. In the first stage, in-sample model performance is evaluated using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and log-likelihood values. All models are estimated using a training sample of 3,999 observations (80% of the dataset). The second stage focuses on out-of-sample forecast accuracy using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) on a hold-out test sample of 1,000 observations (20%) covering the period from March 2021 to March 2025. The empirical findings indicate significant deviations from normality in NIFTY 50 index returns, characterized by fat tails and leverage effects, with excess kurtosis equal to 12.98 and skewness equal to −0.356. Among the models considered, the EGARCH(1,1) model provides the best in-sample fit with a log-likelihood value of 12,250.3 and an AIC value of −24,492.5. Furthermore, it achieves the minimum out-of-sample forecasting errors at the volatility level, with annualized RMSE and MAE values of 3.165% and 2.466%, respectively, followed closely by the GJR-GARCH model. The study also reports an asymmetry ratio of 4.65× for the GJR-GARCH model, highlighting the presence of asymmetric volatility effects. Additionally, the estimated parameters of the Heston Stochastic Volatility model are found to be structurally relevant for derivative pricing applications, with parameter estimates given by ρ = −0.165 and σv =0.44.