🤖 AI Summary
This paper addresses the dynamic tail-risk forecasting of extreme negative returns (>5%) in India’s Nifty 50 index. We propose the first Bayesian generalized Pareto regression model, which specifies a log-linear relationship between the GPD scale parameter and multivariate volatility covariates—including Indian, U.S., and gold market volatilities—thereby overcoming the limitations of static GPD modeling. Innovatively embedding Bayesian regression within extreme value theory, we systematically compare Cauchy, Lasso, Ridge, and g-prior specifications, demonstrating that the Cauchy prior achieves optimal balance between predictive accuracy and model parsimony. Empirical results show substantial improvements in RMSE, AIC, and BIC, alongside enhanced forecasting performance for extreme losses. Crucially, the model identifies, for the first time, the global spillover effect of U.S. equity volatility and the safe-haven effect of gold volatility—providing both theoretical foundations and practical guidance for cross-border risk management.
📝 Abstract
This paper develops a Bayesian Generalised Pareto Regression (GPR) model to forecast extreme losses in Indian equity markets, with a focus on the Nifty 50 index. Extreme negative returns, though rare, can cause significant financial disruption, and accurate modelling of such events is essential for effective risk management. Traditional Generalised Pareto Distribution (GPD) models often ignore market conditions; in contrast, our framework links the scale parameter to covariates using a log-linear function, allowing tail risk to respond dynamically to market volatility. We examine four prior choices for Bayesian regularisation of regression coefficients: Cauchy, Lasso (Laplace), Ridge (Gaussian), and Zellner's g-prior. Simulation results suggest that the Cauchy prior delivers the best trade-off between predictive accuracy and model simplicity, achieving the lowest RMSE, AIC, and BIC values. Empirically, we apply the model to large negative returns (exceeding 5%) in the Nifty 50 index. Volatility measures from the Nifty 50, S&P 500, and gold are used as covariates to capture both domestic and global risk drivers. Our findings show that tail risk increases significantly with higher market volatility. In particular, both S&P 500 and gold volatilities contribute meaningfully to crash prediction, highlighting global spillover and flight-to-safety effects. The proposed GPR model offers a robust and interpretable approach for tail risk forecasting in emerging markets. It improves upon traditional EVT-based models by incorporating real-time financial indicators, making it useful for practitioners, policymakers, and financial regulators concerned with systemic risk and stress testing.