Close the VaR calibration gap by improving tail modeling in NeuralFactors

Develop extensions to the NeuralFactors conditional generative model of equity returns that more accurately capture heavy-tailed behaviour so that predictive quantiles are well calibrated under the calibration error metric used for Value-at-Risk analysis. Specifically, modify the modeling of factor returns and idiosyncratic components within NeuralFactors to reduce the observed calibration error for both individual securities and equal-weighted portfolios, addressing the incomplete tail modeling identified by the authors.

Background

The paper evaluates NeuralFactors on Value-at-Risk (VaR) by measuring calibration error across 100 quantiles, both at the individual security level and for an equal-weighted portfolio. While NeuralFactors performs well on covariance forecasting and achieves strong test-set calibration compared to some baselines, its portfolio calibration error is still worse than the best-performing model (GARCH), indicating a deficiency in modeling extreme outcomes.

This discrepancy suggests that NeuralFactors does not fully capture the heavy tails of equity return distributions, which are crucial for accurate risk quantiles. The authors explicitly call for future work to close this performance gap, making improved tail modeling within the NeuralFactors framework a concrete unresolved problem motivated by the VaR evaluation results.