Backtesting Value-at-Risk: A Comparison between Filtered Bootstrap and Historical Simulation

Abstract

The purpose of this paper is to present a comparison between two risk models for estimating VaR, Historical Simulation and Monte Carlo Filtered Bootstrap. We perform three tests, Unconditional Coverage, Independence and Conditional Coverage according to Christoffersen, P., Pellettier D. (2004) paper. We present results on both VaR 1% and VaR 5% on one day horizon for the two models for the following indices: Standard&Poors 500, Topix, Dax, MSCI United Kingdom, MSCI France, Italy Comit Globale, MSCI Canada, MSCI Emerging Markets, RJ/CRB. Our results show that Filtered Bootstrap Approach satisfy Conditional Coverage for all tested indices while Historical Simulation has many rejection cases. Finally we also tested in a regulatory framework (rolling window of 250 daily observations) the two models and the advantages of using a conditional coverage methodology to validate risk models.

Keywords: VaR, backtest, historical simulation, filtered bootstrap, unconditional coverage, independence