Predicting Stock Market Crash with Bayesian Generalised Pareto Regression

ArXiv ID: 2506.17549 “View on arXiv”

Authors: Sourish Das

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.

Keywords: Bayesian Generalised Pareto Regression, Extreme Value Theory (EVT), Tail Risk, VaR / ES, Volatility Modelling, Equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced Bayesian statistical methods and specialized survival function derivations (high math complexity), and includes a detailed simulation study, multiple volatility estimators, and backtest-ready metrics like RMSE, AIC, and BIC (high empirical rigor).

  flowchart TD
    A["Research Goal<br>Predict Stock Market Crashes<br>using Extreme Value Theory"] --> B{"Data & Inputs"};
    
    B --> B1["Nifty 50 Index<br>(Daily Returns)"];
    B --> B2["Covariates<br>VIX India, S&P 500 Vol, Gold Vol"];
    B --> B3["Threshold Selection<br>Exceedances > 5% Loss"];
    
    A --> C["Methodology<br>Bayesian Generalised Pareto Regression GPR"];
    
    C --> D["Computational Process<br>Prior Comparison & Fitting"];
    
    D --> D1["Priors: Cauchy, Lasso, Ridge, g-Prior"];
    D --> D2["Simulation for Model Selection"];
    
    D1 --> D3["Model Metrics:<br>RMSE, AIC, BIC"];
    D2 --> D3;
    
    D3 --> E{"Key Findings & Outcomes"};
    
    E --> E1["Optimal Model:<br>Cauchy Prior"];
    E --> E2["Risk Drivers:<br>High Volatility increases Crash Risk"];
    E --> E3["Global Spillover:<br>S&P 500 & Gold Volatility significant"];
    E --> E4["Outcome:<br>Robust Tail Risk Forecasting Framework"];