Comparative Backtesting of Value-at-Risk and Expected Shortfall Models Across the US, UK, and India (2005–2025)

This study presents a comprehensive empirical analysis of Value-at-Risk (VaR) and Expected Shortfall (ES) models across three major equity indices: S&P 500 (US), FTSE 100 (UK), and NIFTY 50 (India) over the period 2005–2025. We implement and backtest five different risk modeling approaches: Historical Simulation, Parametric Normal, Parametric Student-t, GARCH(1,1) with Student-t innovations, and Extreme Value Theory using Peaks-over-Threshold. The backtesting framework employs regulatory-standard tests including Kupiec's Proportion of Failures test, Christoffersen's Independence and Conditional Coverage tests, and the Basel Committee's Traffic Light approach. Our results reveal significant differences in model performance across markets and time periods, with particular emphasis on periods of financial stress including the 2007– 2009 Global Financial Crisis and the 2020 COVID-19 pandemic. The study provides practical insights for risk managers and regulators on the comparative effectiveness of different VaR methodologies across developed and emerging markets.