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Bayesian Forecasting of Value at Risk and Expected Shortfall using Adaptive Importance Sampling

Lennart Hoogerheide () and Herman van Dijk ()
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Lennart Hoogerheide: Erasmus University Rotterdam

No 08-092/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: This discussion paper resulted in a publication in the International Journal of Forecasting , 2010, 26(2), 231-247.

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.

Keywords: Value at Risk; Expected Shortfall; numerical accuracy; numerical standard error; importance sampling; mixture of Student-t distributions; variance reduction technique (search for similar items in EconPapers)
JEL-codes: C11 C15 C53 D81 (search for similar items in EconPapers)
Date: 2008-10-02
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Journal Article: Bayesian forecasting of Value at Risk and Expected Shortfall using adaptive importance sampling (2010) Downloads
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