Bayesian Forecasting of Value at Risk and Expected Shortfall using Adaptive Importance Sampling
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.
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|Tinbergen Institute Discussion Paper Series|
|Discussion paper / Tinbergen Institute|
Hoogerheide, L.F, & van Dijk, H.K. (2008). Bayesian Forecasting of Value at Risk and Expected Shortfall using Adaptive Importance Sampling (No. TI 2008-092/4). Discussion paper / Tinbergen Institute. Tinbergen Institute. Retrieved from http://hdl.handle.net/1765/14045