Assessing the Price Volatility in the Top 50 Blue Chip Companies of Nifty Index - An Analysis using GARCH and ARCH Model

Abstract

This research has been conducted to study Nifty 50 index price volatility dynamics through the application of ARCH, GARCH and Heston stochastic volatility modelling approaches. Financial decision-makers including investors along with institutions and policymakers need volatility as a cornerstone for their decisions. The research uses conventional daily closing prices between 2010 and 2025 to demonstrate volatility clustering through standard ARCH and GARCH models. This analysis shows GARCH offers superior results over ARCH when demonstrating volatility persistence but it does not meet emerging market requirements toward fully explaining asymmetry along with memory features typically found in Indian financial markets. The research solves these issues by using the Heston stochastic volatility model that handles mean reversion and stochastic variance evolution along with leverage effects. The Heston model delivers advanced volatility behaviour analysis while maintaining practicality and effectiveness of GARCH models during regular market applications. Due to its complex nature Heston needs advanced skills for its application yet proves better suited for complex modelling situations instead of basic forecasting tasks.

Introduction

The study focuses on analyzing the volatility of the Nifty 50 index, which reflects the performance of the Indian equity market. Volatility is a key factor in investment decisions, risk management, asset pricing, and financial regulation. The Nifty 50, composed of India’s top 50 companies, serves as a benchmark index and is a critical tool for evaluating market risk and economic stability.

Volatility Modelling: ARCH, GARCH, and Limitations

• ARCH (Autoregressive Conditional Heteroskedasticity) and GARCH (Generalized ARCH) models are widely used econometric tools for modeling financial volatility.

• ARCH links current volatility to past squared errors, while GARCH incorporates both past errors and past variances.

• These models, though useful, have limitations:

  • They assume symmetrical reactions to positive and negative shocks, which doesn’t reflect real markets.

  • They assume short memory, while emerging markets like India exhibit long memory effects and regime shifts.

  • They cannot capture leverage effects or sudden structural breaks accurately.

Need for Improved Models

Standard ARCH/GARCH models are insufficient for fully capturing the volatility of Indian markets. The study proposes exploring hybrid and more sophisticated models, such as the Heston Stochastic Volatility Model, which accounts for:

• Mean-reverting volatility,

• Time-varying variance,

• Leverage effect,

• Correlation between asset prices and volatility.

Literature Review

Numerous studies have applied ARCH and GARCH models to Indian stock market data, confirming the presence of volatility clustering and asymmetry. However, most have not addressed long memory, structural changes, or hybrid model integration. Recent research suggests incorporating machine learning techniques (e.g., ANN, LSTM) into volatility models to improve forecasting accuracy.

Research Objectives

1. Analyze Nifty 50 price volatility using ARCH and GARCH.

2. Test hybrid models that handle long-term trends, asymmetries, and abrupt market changes.

Methodology

• Data: Daily closing prices of the Nifty 50 index (2010–2025), sourced from NSE, Yahoo Finance, and Investing.com.

• Data Processing: Prices were converted to log returns to achieve stationarity.

• Models used:

  • ARCH for detecting volatility from past squared returns.

  • GARCH to model persistent volatility.

  • Heston Model to simulate stochastic, mean-reverting volatility with leverage effects.

Model Findings

• ARCH Model: Captures volatility spikes but overreacts and lacks smoothness.

  • Log-Likelihood: 11,858.1

  • AIC: –23,710.2

• GARCH Model: Better fits the data with smooth clustering and long memory.

  • Log-Likelihood: 12,130.1

  • AIC: –24,252.2

  • α? + β? = 0.98 → High persistence

• Heston Model: Captures real market behavior more accurately (mean reversion, leverage effect) and fits rolling volatility well.

Diagnostics

• ACF/PACF plots of squared standardized residuals show no remaining autocorrelation, validating the GARCH model.

• Q-Q plots suggest residuals are approximately normally distributed.

Conclusion

This study compared three volatility models ARCH, GARCH and the Heston stochastic model on the Nifty 50 index. ARCH offers a basic model of time-varying volatility, but lacks longterm memory. GARCH improves upon this by incorporating persistence, offering better fit and smoother volatility estimates. However, both are discrete-time models and do not account for the stochastic nature of volatility. The Heston model, with its continuous-time stochastic volatility framework, captures deeper market behaviours like mean-reverting volatility and leverage effects. While the Heston model offers theoretical and practical advantages, its complexity and calibration challenges remain barriers. In conclusion, for practical applications with limited computational resources, GARCH remains a robust choice. For advanced modelling needs, especially in derivative pricing and risk management, Heston offers superior modelling fidelity.

References

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Copyright

Copyright © 2025 Prathvi Annappa Hegde, Mrs. Uma Sharma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.