Journal of Risk Model Validation

Backtesting value-at-risk: a comparison between filtered bootstrap and historical simulation

Dario Brandolini and Stefano Colucci


The purpose of this paper is to compare ex ante value-at-risk (VaR) estimation produced by two risk models: historical simulation and Monte Carlo filtered bootstrap. We perform three tests: unconditional coverage, independence and conditional coverage. We present results on both VaR1% and VaR5% on a one-day horizon for the following indexes: S&P 500, Topix, Dax, MSCI United Kingdom, MSCI France, Italy Comit Globale, MSCI Canada, MSCI Emerging Markets and RJ/CRB. Our results show that the Monte Carlo filtered bootstrap approach satisfies conditional coverage for all tested indexes, while historical simulation has many rejection cases. We also test the two models in a regulatory framework (rolling window of 250 daily observations) and discuss the advantages of using a conditional coverage methodology to validate risk models.

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