Estimating value-at-risk: LSTM vs. GARCH

Abstract

Estimating value-at-risk on time series data with potentially heteroskedastic dynamics is a highly challenging task. In practical applications, one often faces limited sample sizes in combination with a high degree of non-linearity, which poses difficulties for both classical and machine-learning-based estimation algorithms. In this paper, we propose a novel non-parametric value-at-risk estimator based on a long short-term memory (LSTM) neural network and compare its performance against a benchmark set of estimators, including empirical quantile, Gaussian, and parametric GARCH-based approaches. Our results indicate that the proposed LSTM-based estimator is able to recover GARCH-like conditional risk dynamics when evaluated on simulated data generated from parametric volatility models. In empirical applications to market data, the LSTM-based value-at-risk forecasts exhibit calibration properties comparable to those of classical parametric benchmarks and frequently achieve lower average quantile scores, suggesting improved tail risk assessment. Moreover, the qualitative alignment between LSTM-based and GARCH-based risk projections persists across alternative GARCH-type specifications, indicating that the observed performance is not driven by a particular parametric model choice. Taken together, these findings support the use of LSTM-based estimators as a flexible and robust non-parametric tool for value-at-risk estimation or monitoring in environments characterized by time-varying volatility.