Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests

Elena Ivona Dumitrescu, Christophe Hurlin and Vinson Pham
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Vinson Pham: UC Santa Cruz - University of California [Santa Cruz] - UC - University of California

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Abstract: In this paper we propose a new tool for backtesting that examines the quality of Value-at- Risk (VaR) forecasts. To date, the most distinguished regression-based backtest, proposed by Engle and Manganelli (2004), relies on a linear model. However, in view of the di- chotomic character of the series of violations, a non-linear model seems more appropriate. In this paper we thus propose a new tool for backtesting (denoted DB) based on a dy- namic binary regression model. Our discrete-choice model, e.g. Probit, Logit, links the sequence of violations to a set of explanatory variables including the lagged VaR and the lagged violations in particular. It allows us to separately test the unconditional coverage, the independence and the conditional coverage hypotheses and it is easy to implement. Monte-Carlo experiments show that the DB test exhibits good small sample properties in realistic sample settings (5% coverage rate with estimation risk). An application on a portfolio composed of three assets included in the CAC40 market index is nally proposed.

Keywords: Value-at-Risk; Risk Management; Dynamic Binary Choice Models (search for similar items in EconPapers)
Date: 2012-02-07
New Economics Papers: this item is included in nep-ban, nep-ecm and nep-rmg
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00671658v1
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Citations: View citations in EconPapers (26)

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Journal Article: Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests (2012)
Working Paper: Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests (2012)
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