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A comparison of Bayesian approaches to forecasting Value-at-Risk

Bergling, Elis LU (2026) In Bachelor’s Theses in Mathematical Sciences FMSL01 20261
Mathematical Statistics
Abstract
Reliable Value-at-Risk forecasts are essential for quantifying the market risk a financial institution is exposed to. Utilizing a Bayesian approach treats the model's parameters as random variables, allowing for forecasts that consider parameter uncertainty as well as a measure of uncertainty through the spread of the forecasts, the epistemic uncertainty. The method of approximating the parameter uncertainty does, however, vary widely between low-dimensional parametric models and high-dimensional neural networks, and this thesis aims to compare them applied to a GARCH model using Markov chain Monte Carlo (MCMC) and an LSTM using Monte Carlo Dropout (MC Dropout). They are compared to their non-Bayesian counterparts using Christoffersen's... (More)
Reliable Value-at-Risk forecasts are essential for quantifying the market risk a financial institution is exposed to. Utilizing a Bayesian approach treats the model's parameters as random variables, allowing for forecasts that consider parameter uncertainty as well as a measure of uncertainty through the spread of the forecasts, the epistemic uncertainty. The method of approximating the parameter uncertainty does, however, vary widely between low-dimensional parametric models and high-dimensional neural networks, and this thesis aims to compare them applied to a GARCH model using Markov chain Monte Carlo (MCMC) and an LSTM using Monte Carlo Dropout (MC Dropout). They are compared to their non-Bayesian counterparts using Christoffersen's conditional coverage framework and quantile loss over the 1\% and 5\% VaR levels, and evaluated on overall predictive performance using the discretized continuous ranked probability score (CRPS), on a one-day horizon across three assets. A characterization of the epistemic uncertainty and its relation to predictive performance is also performed.

The Bayesian model in the GARCH family exhibited better predictive accuracy in quantile loss and CRPS, whereas the Bayesian framework showed the opposite, but more weakly, when applied to the LSTM. As for tests within the conditional coverage framework, no results favoured either approach. The models performed worse on the loss-based scores when their epistemic uncertainty was high, even after accounting for the level of realized volatility, though the effect was weakened. The overall conclusion is that the propagation of uncertainty is only useful for the GARCH, and both signals of epistemic uncertainty are informative about the reliability of the models. (Less)
Please use this url to cite or link to this publication:
author
Bergling, Elis LU
supervisor
organization
course
FMSL01 20261
year
type
M2 - Bachelor Degree
subject
keywords
Value-at-Risk, Bayesian inference, GARCH, LSTM, epistemic uncertainty
publication/series
Bachelor’s Theses in Mathematical Sciences
report number
LUTFMS-4021-2026
ISSN
1654-6229
other publication id
2026:27
language
English
id
9250706
date added to LUP
2026-09-10 12:37:03
date last changed
2026-09-10 13:18:43
@misc{9250706,
  abstract     = {{Reliable Value-at-Risk forecasts are essential for quantifying the market risk a financial institution is exposed to. Utilizing a Bayesian approach treats the model's parameters as random variables, allowing for forecasts that consider parameter uncertainty as well as a measure of uncertainty through the spread of the forecasts, the epistemic uncertainty. The method of approximating the parameter uncertainty does, however, vary widely between low-dimensional parametric models and high-dimensional neural networks, and this thesis aims to compare them applied to a GARCH model using Markov chain Monte Carlo (MCMC) and an LSTM using Monte Carlo Dropout (MC Dropout). They are compared to their non-Bayesian counterparts using Christoffersen's conditional coverage framework and quantile loss over the 1\% and 5\% VaR levels, and evaluated on overall predictive performance using the discretized continuous ranked probability score (CRPS), on a one-day horizon across three assets. A characterization of the epistemic uncertainty and its relation to predictive performance is also performed.
 
The Bayesian model in the GARCH family exhibited better predictive accuracy in quantile loss and CRPS, whereas the Bayesian framework showed the opposite, but more weakly, when applied to the LSTM. As for tests within the conditional coverage framework, no results favoured either approach. The models performed worse on the loss-based scores when their epistemic uncertainty was high, even after accounting for the level of realized volatility, though the effect was weakened. The overall conclusion is that the propagation of uncertainty is only useful for the GARCH, and both signals of epistemic uncertainty are informative about the reliability of the models.}},
  author       = {{Bergling, Elis}},
  issn         = {{1654-6229}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Bachelor’s Theses in Mathematical Sciences}},
  title        = {{A comparison of Bayesian approaches to forecasting Value-at-Risk}},
  year         = {{2026}},
}