Bridging Econometrics and AI: VaR Estimation via Reinforcement Learning and GARCH Models

Context: Forecasting stock returns is a long-standing challenge in financial economics, with significant implications for both risk management and regulatory compliance. Traditional econometric models such as GARCH (Bollerslev, 1986) capture volatility persistence but fail to fully account for key stylized facts of financial time series: fat tails, volatility clustering, and leverage effects (Glosten et al., 1993). Similarly, modern machine learning and deep learning methods, although capable of modeling nonlinear dynamics (Goodfellow et al., 2016; Tealab, 2018), tend to underperform during rare but impactful market shocks (Fawcett and Provost, 1997; Pokou, 2022). As illustrated in Figure 1, these limitations often result in systematic mispredictions of excess returns, especially in turbulent markets. These forecasting inaccuracies are critical because they directly translate into unreliable estimates of Value-at-Risk (VaR), the benchmark risk measure under Basel regulatory frameworks (on Banking Supervision, 2017). Overestimation inflates capital requirements, whereas underestimation exposes institutions to excessive losses. To mitigate these shortcomings, the recent literature has shifted from precise return forecasting to directional return prediction, reframe the task as a classification problem, determining whether returns will be positive or negative (Kanas, 2001; Nyberg, 2011; Alostad and Davulcu, 2017). Beyond the standard zero threshold, quantile and volatility-based criteria have been introduced to better isolate significant market movements (Chung and Hong, 2007; Linton and Whang, 2007).