A Hybrid Fractional Artificial Neural Network Model for Value at Risk Prediction in Emerging Financial Markets

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Objective: This study aims to develop an improved methodology for forecasting Value at Risk (VaR) by addressing the limitations of traditional risk-measurement models that fail to capture long-memory behavior and nonlinear dependencies in financial returns. The objective is to integrate fractional calculus with Artificial Neural Networks (ANNs) to produce more accurate and reliable VaR estimates for major Indian stock indices. Methodology: Daily return data from the NIFTY 50 and SENSEX indices were used to construct fractional-order features that represent long-memory dynamics. These features were then fed into an ANN trained using quantile loss to directly estimate VaR at 95% and 99% confidence levels. Model performance was evaluated through standard backtesting procedures, including the Kupiec Proportion of Failures (POF) test and Christoffersen’s conditional coverage test, and compared against variance–covariance, Historical Simulation, and GARCH-type models. Originality: This research provides a novel hybrid risk-forecasting framework that combines fractional calculus with ANN-based nonlinear modeling an approach rarely applied in VaR estimation. By explicitly incorporating long-memory dependence structures and nonlinear residual patterns, the study extends existing risk-management literature beyond conventional econometric and machinelearning models, offering a more robust methodology for volatile and crisis-prone markets. Main Results: The hybrid fractional-ANN model significantly outperforms traditional VaR techniques, yielding more accurate tail-risk estimates with fewer exceedances. Backtesting results confirm that the proposed model satisfies both unconditional and conditional coverage requirements more consistently than benchmark models. These findings demonstrate that integrating long-memory features and nonlinear learning capabilities enhances the reliability of VaR forecasts, particularly during periods of heightened market volatility. Theoretical Contributions: This study advances risk-management theory by introducing a unified framework that bridges fractional-order financial modeling with quantile-based neural networks. It highlights the importance of long-range dependence and nonlinear dynamics in tail-risk estimation and establishes a foundation for future research on fractional-machine-learning hybrid models in financial econometrics. The work contributes to modern risk-forecasting methodologies suitable for regulatory and institutional applications.

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