Evaluating Value-at-Risk Models via Quantile Regression

• Published in: Journal of business & economic statistics Vol. 29; no. 1; pp. 150 - 160
• Main Authors: Gaglianone, Wagner Piazza, Lima, Luiz Renato, Linton, Oliver, Smith, Daniel R.
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 01-01-2011; American Statistical Association; Taylor & Francis Ltd
• Subjects: Backtesting; Binary system; Economic models; Economic statistics; Investment risk; Modeling; Monte Carlo simulation; Null hypothesis; Orthogonality; Quantile regression; Quantiles; Regression analysis; Risk exposure; Sample size; Studies; Time series
• ISSN: 0735-0015; 1537-2707
• DOI: 10.1198/jbes.2010.07318

This article is concerned with evaluating Value-at-Risk estimates. It is well known that using only binary variables, such as whether or not there was an exception, sacrifices too much information. However, most of the specification tests (also called backtests) available in the literature, such as Christoffersen (1998) and Engle and Manganelli (2004) are based on such variables. In this article we propose a new backtest that does not rely solely on binary variables. It is shown that the new backtest provides a sufficient condition to assess the finite sample performance of a quantile model whereas the existing ones do not. The proposed methodology allows us to identify periods of an increased risk exposure based on a quantile regression model (Koenker and Xiao 2002). Our theoretical findings are corroborated through a Monte Carlo simulation and an empirical exercise with daily S&P500 time series.