Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/87093
Authors: 
Hoogerheide, Lennart
van Dijk, Herman K.
Year of Publication: 
2008
Series/Report no.: 
Tinbergen Institute Discussion Paper 08-092/4
Abstract: 
An efficient and accurate approach is proposed for forecasting Value at Risk [VaR] and Expected Shortfall [ES] measures in a Bayesian framework. This consists of a new adaptive importance sampling method for Quantile Estimation via Rapid Mixture of t approximations [QERMit]. As a first step the optimal importance density is approximated, after which multi-step `high loss' scenarios are efficiently generated. Numerical standard errors are compared in simple illustrations and in an empirical GARCH model with Student-t errors for daily S&P 500 returns. The results indicate that the proposed QERMit approach outperforms several alternative approaches in the sense of more accurate VaR and ES estimates given the same amount of computing time, or equivalently requiring less computing time for the same numerical accuracy.
Subjects: 
Value at Risk
Expected Shortfall
numerical accuracy
numerical standard error
importance sampling
mixture of Student-t distributions
variance reduction technique
JEL: 
C11
C15
C53
D81
Document Type: 
Working Paper

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