Volatility Modelling of the BSE SENSEX Using the ARCH Model: An Empirical Study of Select Large-Cap Constituent Stocks (2021–2026)

Abstract

Stock market volatility is of continuing interest to investors, portfolio managers, corporates and policymakers because it directly influences risk assessment, asset pricing and capital allocation decisions. This paper examines the return-generating and volatility process of the Bombay Stock Exchange Sensitive Index (BSE SENSEX) using the Autoregressive Conditional Heteroskedasticity (ARCH) model of Engle (1982), estimated separately for five consecutive financial years spanning April 2021 to January 2026. Daily closing prices of the SENSEX and ten actively traded, large-capitalisation constituent stocks were employed as explanatory variables in the mean equation, while the conditional variance was modelled as a GARCH(1,1)-type specification and estimated through Maximum Likelihood in EViews. The results show that the ARCH coefficient is positive and statistically significant in four of the five years, confirming the presence of volatility clustering in SENSEX returns, whereas the GARCH persistence term is small and, in three of the five years, negative, implying that shocks to variance die out quickly rather than persisting. The explanatory power of the mean equation ranged between 0.69 and 0.81 across the five years, and descriptive statistics of daily returns confirm negative skewness and excess kurtosis, validating the use of an ARCH-family model over ordinary least squares. The findings carry implications for risk management, portfolio diversification and short-horizon volatility forecasting in the Indian equity market.