Standard and stressed value at risk forecasting using dynamic Bayesian networks
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.
Summary
This paper investigates the use of dynamic Bayesian networks (DBNs) for forecasting Value at Risk (VaR) and stressed Value at Risk (SVaR) for the S&P 500 index, comparing their performance to traditional models. The main research question is whether DBNs, incorporating forward-looking return forecasts, can improve upon the accuracy of traditional VaR and SVaR forecasting methods. The authors utilize daily S&P 500 index returns from 1991 to 2020, constructing 10-day 99% VaR and SVaR forecasts using a rolling period. Traditional models rely on historical returns, while DBNs incorporate both historical and forecasted returns. Three different DBN learning algorithms are tested. The models' forecasting accuracy is evaluated using backtesting techniques (BCBS traffic light test, Kupiec's proportion of failure test, Christoffersen's test for independence) and forecasting error measures (MAE, RMSE, MAPE). The key finding is that autoregressive models, specifically EGARCH, deliver the most accurate VaR forecasts, while DBNs achieve comparable performance to the historical simulation model, even though DBNs incorporate forward-looking information. For SVaR, all models produce highly conservative forecasts with minimal breaches, making it difficult to differentiate their accuracy. While DBNs do not outperform traditional models in this specific application, the study demonstrates the feasibility of DBNs as a forward-looking approach for financial risk forecasting, paving the way for future research integrating causal inference into the process. This matters to the field because it explores a novel approach to risk management and suggests potential avenues for improving risk forecasting by incorporating forward-looking information and causal relationships.
Key Insights
- •DBNs, despite their ability to incorporate forward-looking return forecasts, do not outperform traditional autoregressive models (specifically EGARCH) in forecasting VaR for the S&P 500 index. The EGARCH model using a normal distribution had the lowest MAE (0.0694), RMSE (0.0776), and MAPE (59.719%).
- •All models, including DBNs, produce highly conservative SVaR forecasts, resulting in minimal breaches and making it difficult to differentiate their performance.
- •The study adopts a conservative approach to constructing the stressed period for SVaR, amalgamating days with the worst returns, which contributes to the existing literature on SVaR estimation.
- •The BCBS traffic light test is found to be an inadequate measure for differentiating model accuracy, as all models tested pass with a 'Green zone' outcome due to the low number of breaches.
- •The study demonstrates the feasibility of DBNs for financial risk forecasting, providing a practical application of the methodology and serving as a foundation for future research integrating causal inference.
- •The historical simulation model, widely used by banks, performs poorly in terms of forecasting error measures (MAE 0.0944, RMSE 0.1003, MAPE 98.135%), confirming its limitations in capturing market volatility.
- •Using the skewed Student's t distribution instead of the normal distribution doesn't consistently improve the forecasting accuracy of autoregressive models; some models (GARCH, EGARCH, RiskMetrics) show a decrease in accuracy.
Practical Implications
- •While DBNs did not outperform traditional models in this specific study, the research opens up possibilities for exploring more sophisticated DBN architectures and variable selection techniques to improve forecasting accuracy.
- •The conservative nature of SVaR forecasts suggests a need for developing more sensitive risk measures that can better capture tail risk and adapt to changing market conditions.
- •Risk managers and financial institutions can benefit from exploring DBNs as a complementary tool for risk assessment, particularly for incorporating forward-looking information and understanding causal relationships.
- •Future research should focus on integrating causal inference techniques into DBNs to improve their ability to predict market risk and adapt to regime-switching behavior during financial crises.
- •The findings highlight the limitations of relying solely on the BCBS traffic light test for model validation, emphasizing the importance of using a comprehensive suite of backtesting techniques and forecasting error measures.