Bootstrap prediction intervals for VaR and ES in the context of GARCH models
AbstractIn this paper, we propose a new bootstrap procedure to obtain prediction intervals of future Value at Risk (VaR) and Expected Shortfall (ES) in the context of univariate GARCH models. These intervals incorporate the parameter uncertainty associated with the estimation of the conditional variance of returns. Furthermore, they do not depend on any particular assumption on the error distribution. Alternative bootstrap intervals previously proposed in the literature incorporate the first but not the second source of uncertainty when computing the VaR and ES. We also consider an iterated smoothed bootstrap with better properties than traditional ones when computing prediction intervals for quantiles. However, this latter procedure depends on parameters that have to be arbitrarily chosen and is very complicated computationally. We analyze the finite sample performance of the proposed procedure and show that the coverage of our proposed procedure is closer to the nominal than that of the alternatives. All the results are illustrated by obtaining one-step-ahead prediction intervals of the VaR and ES of several real time series of financial returns.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws102814.
Date of creation: May 2010
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Expected Shortfall; Feasible Historical Simulation; Hill estimator; Parameter uncertainty; Quantile intervals; Value at Risk;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-06-04 (All new papers)
- NEP-ECM-2010-06-04 (Econometrics)
- NEP-FOR-2010-06-04 (Forecasting)
- NEP-RMG-2010-06-04 (Risk Management)
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