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Evaluating Value-at-Risk models via Quantile Regression

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  • Gaglianone, Wagner Piazza
  • Lima, Luiz Renato
  • Linton, Oliver
  • Smith, Daniel

Abstract

This paper 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 Maganelli (2004) are based on such variables. In this paper 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 & Xiao, 2002). Our theoretical findings are corroborated through a Monte Carlo simulation and an empirical exercise with daily S&P500 time series.

Suggested Citation

  • Gaglianone, Wagner Piazza & Lima, Luiz Renato & Linton, Oliver & Smith, Daniel, 2009. "Evaluating Value-at-Risk models via Quantile Regression," UC3M Working papers. Economics we094625, Universidad Carlos III de Madrid. Departamento de Economía.
  • Handle: RePEc:cte:werepe:we094625
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    More about this item

    Keywords

    Value-at-Risk;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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