Uncertainty in Value-at-Risk Estimates Under Parametric and Non-Parametric Modeling
31 Pages Posted: 26 Feb 2005
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Uncertainty in Value-at-Risk Estimates Under Parametric and Non-Parametric Modeling
Uncertainty in Value-at-Risk Estimates Under Parametric and Non-Parametric Modeling
Date Written: April 2006
Abstract
This study evaluates a set of parametric and non-parametric Value-at-Risk (VaR) models that quantify the uncertainty in VaR estimates in form of a VaR distribution. We propose a new VaR approach based on Bayesian statistics in a GARCH volatility modeling environment. This Bayesian approach is compared with other parametric VaR methods (quasi-maximum likelihood and bootstrap resampling on the basis of GARCH models) as well as with non-parametric historical simulation approaches (classical and volatility adjusted). All these methods are evaluated based on the frequency of failures and the uncertainty in VaR estimates.
Within the parametric methods, the Bayesian approach is better able to produce adequate VaR estimates, and results mostly in a smaller VaR variability. The non-parametric methods imply more uncertain 99%-VaR estimates, but show good performance with respect to 95%-VaRs.
Keywords: Value-at-Risk, Bayesian analysis, GARCH, Historical Simulation, Bootstrap resampling
JEL Classification: C11, C50, G10
Suggested Citation: Suggested Citation
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