Prognozowanie oczekiwanej straty dla surowców energetycznych przy użyciu regresji kwantylowej  
[Forecasting expected shortfall for energy commodities using quantile regression]

Sjur Westgaard (Department of Industrial Economics & Technology Management, NTNU, Trondheim, NOR)


Expected Shortfall (ES) offers significant advantages over Value at Risk (VaR) by addressing the 
latter's limitations in capturing tail risks beyond a specified quantile. While VaR estimates 
the maximum potential loss within a certain confidence level, ES provides the average loss 
beyond this threshold, offering a more comprehensive measure of extreme risks. Furthermore, ES 
is subadditive, making it a more reliable tool in risk management (Artzner, 1997; Artzner et 
al., 1999). Due to these benefits, ES has gained increasing importance and is now widely adopted 
in risk assessment frameworks. The Basel Committee (2013) even recommends transitioning from VaR 
to ES in quantitative risk metrics. Scenario analysis and stress testing are crucial for 
financial institutions to gauge the impact of extreme events, such as economic downturns and 
market crashes (Basel, 2010). These methods help institutions identify vulnerabilities and 
assess the effectiveness of their risk management strategies. As a result, there is a growing 
demand for robust risk models that can forecast both VaR and ES, while also analyzing the 
influence of various risk factors on these metrics. Quantile regression models, which estimate 
VaR and ES jointly while incorporating covariates, have been recently developed by Fissler and 
Ziegel (2016) and Dimitriadis and Bayer (2019). These models facilitate direct scenario analysis 
and stress testing of risk factors. The R package "esreg" (Bayer and Dimitriadis, 2024) 
implements these methodologies, and a joint test for VaR and ES prediction is available in the 
"esback" package (Bayer and Dimitriadis, 2023). This paper explores the implementation of these 
methods in estimating VaR and ES jointly for oil, natural gas, electricity, and coal futures. It 
also examines the impact of risk factors such as return volatility and forward curve slope 
volatility on the lower and upper tail risks of different energy commodities.