International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 12 Issue: 06 | Jun 2025
p-ISSN: 2395-0072
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Analyzing Volatility in the NIFTY 50 Index with ARCH and GARCH Models: A Two-Decade Perspective Shubham Nikam1, Sunny Nahar2 1Dept of Master of Computer Applications, VES’s Institute of Technology, Chembur- 400074 2Assistant Professor, Dept of Master of Computer Applications, VES’s Institute of Technology, Chembur- 400074 ---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - This paper investigates how volatility behaves
markets. Jorion (1993) demonstrated the utility of GARCH models in predicting volatility in foreign exchange markets. Kroner and Ng (1998) investigated asymmetric GARCH models to account for negative shocks impacting volatility more than positive ones. In the Indian context, various studies have applied GARCH models to equity indices, often focusing on short time spans or sector-specific volatility. However, few studies extend over a full 20-year period or cover the impact of multiple economic cycles. This paper aims to fill that gap by presenting a comprehensive longterm analysis of volatility in the NIFTY 50 Index using robust econometric tools.
in the NIFTY 50 Index over a 20-year period using ARCH and GARCH models. By analyzing daily log returns derived from historical price data, we explore the evolving nature of market fluctuations. The analysis highlights notable ARCH effects and identifies the GARCH(1,1) model as the most reliable for capturing conditional volatility, as confirmed by lower AIC and BIC values. These f indings contribute insights for managing risk and understanding market behavior in Indian large-cap equities Key Words: ARCH, GARCH, Volatility Modelling, NIFTY 50, Financial Time Series, Econometrics
3. DATA
1. INTRODUCTION
We collected daily historical price data of the NIFTY 50 Index from Yahoo Finance, covering the period from September 26, 2005, to June 6, 2025. The dataset includes adjusted closing prices, which were used to compute daily log returns. This duration captures a range of economic conditions, offering a broad perspective on market dynamics.
Volatility is a fundamental concept in finance, influencing investment decisions, risk management, and regulatory policies. Financial markets, especially those in emerging economies like India, are subject to dynamic structural changes that impact market behavior. The NIFTY 50 Index represents a benchmark portfolio of 50 large-cap Indian stocks. Understanding its volatility behavior provides insight into the broader Indian financial system. Over the past two decades, India has experienced multiple economic transitions, including the global financial crisis (2008), demon etization (2016), and the COVID-19 pandemic (2020), making this period suitable for longterm volatility analysis. In this paper, we employ ARCH and GARCH models to examine volatility clustering in the NIFTY 50 Index and evaluate model performance for volatility forecasting.
3.1 Adjusted Close Prices
2. LITERATURE REVIEW The study of volatility modeling gained prominence with the introduction of the ARCH model by Engle (1982), which enabled analysts to account for time-varying variance in financial returns. Bollerslev (1986) extended this model into the GARCH framework, allowing for the inclusion of both autoregressive and moving average components in variance equations, thereby enhancing its predictive capability.
Fig. 1: Adjusted Close Prices of NIFTY 50 Index
3.2 Daily Log Returns Logarithmic returns are calculated as:
Heston (1996) explored ARCH-type models in the context of option pricing, providing insight into how volatility modeling can improve pricing accuracy in derivative
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