Standard and stressed value at risk forecasting using dynamic Bayesian networks

Paper: arXiv 2512.05661

Authors: Eden Gross, Ryan Kruger, Francois Toerien

Abstract

This study introduces a dynamic Bayesian network (DBN) framework for forecasting value at risk (VaR) and stressed VaR (SVaR) and compares its performance to several commonly applied models. Using daily S&P 500 index returns from 1991 to 2020, we produce 10-day 99% VaR and SVaR forecasts using a rolling period and historical returns for the traditional models, while three DBNs use both historical and forecasted returns. We evaluate the models’ forecasting accuracy using standard backtests and forecasting error measures. Results show that autoregressive models deliver the most accurate VaR forecasts, while the DBNs achieve comparable performance to the historical simulation model, despite incorporating forward-looking return forecasts. For SVaR, all models produce highly conservative forecasts, with minimal breaches and limited differentiation in accuracy. While DBNs do not outperform traditional models, they demonstrate feasibility as a forward-looking approach to provide a foundation for future research on integrating causal inference into financial risk forecasting.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous empirical evaluation of Dynamic Bayesian Networks (DBNs) for forecasting VaR and SVaR using 30 years of S&P 500 data. While DBNs do not outperform traditional autoregressive models, the novel application of causal graphical models for risk metric forecasting is well-documented and evaluated across multiple statistical backtests.

Research Flowchart

  flowchart TD
    A[Research Goal: Forecast VaR & SVaR using DBNs vs. Traditional Models] --> B[Input Data: S&P 500 Daily Returns 1991–2020]
    B --> C[Methodology: Produce 10-day 99% VaR & SVaR Forecasts]
    C --> D[Models Compared: DBNs vs. AR & Historical Simulation]
    D --> E[Model Evaluation: Backtesting & Forecasting Error Analysis]
    E --> F[VaR Finding: AR models most accurate; DBNs comparable to Historical Simulation]
    E --> G[SVaR Finding: All models produce highly conservative, similar forecasts]
    F & G --> H[Outcome: Proves DBN feasibility for forward-looking risk forecasting]

Cited References (36)

1. The Failure of Silicon Valley Bank and the Panic of 2023 (2024) — link
2. Regulatory Capital and Incentives for Risk Model Choice under Basel 3* (2021) — link
3. Forecast combinations for value at risk and expected shortfall (2020) — link
4. Critical Analysis of the New Basel Minimum Capital Requirements for Market Risk (2017) — link
5. An evaluation of bank measures for market risk before, during and after the financial crisis ☆ (2017) — link
6. Frontiers in VaR forecasting and backtesting (2016) — link
7. Evaluation of Basel III revision of quantitative standards for implementation of internal models for market risk (2012) — link
8. Evaluating Value-at-Risk Models with Desk-Level Data (2011) — link

0 of 36 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.