Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2008-10-02 Number: 08-092/4 Author-Name: Lennart Hoogerheide Author-Email: firstname.lastname@example.org Author-Workplace-Name: Erasmus University Rotterdam Author-Name: Herman K. van Dijk Author-Email: email@example.com Author-Workplace-Name: Erasmus University Rotterdam Title: Bayesian Forecasting of Value at Risk and Expected Shortfall using Adaptive Importance Sampling 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. Classification-JEL: C11, C15, C53, D81 Keywords: Value at Risk, Expected Shortfall, numerical accuracy, numerical standard error, importance sampling, mixture of Student-t distributions, variance reduction technique File-Url: http://papers.tinbergen.nl/08092.pdf File-Format: application/pdf File-Size: 2071476 bytes Handle: RePEc:tin:wpaper:20080092