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

36 Pages Posted: 28 Nov 2011 Last revised: 30 Jan 2014

See all articles by Stefano Colucci

Stefano Colucci

Symphonia Sgr; University of Rome III - Department of Business Studies

Dario Brandolini

University of Turin

Date Written: November 28, 2011

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

Suggested Citation

Colucci, Stefano and Brandolini, Dario, Backtesting Value-at-Risk: A Comparison between Filtered Bootstrap and Historical Simulation (November 28, 2011). Available at SSRN: https://ssrn.com/abstract=1965377 or http://dx.doi.org/10.2139/ssrn.1965377

Stefano Colucci (Contact Author)

Symphonia Sgr ( email )

via Gramsci 7
Torino, Torino 10144
Italy

University of Rome III - Department of Business Studies ( email )

Via Silvio D'Amico 77
Via Silvio D'Amico 77
Rome, RM 00145
Italy

Dario Brandolini

University of Turin ( email )

Via Po 53
Torino, Turin - Piedmont 10100
Italy

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