A Residual Bootstrap for Conditional Value-at-Risk

Eric Beutner, Alexander Heinemann, Stephan Smeekes

Research output: Working paperProfessional

Abstract

This paper proposes a fixed-design residual bootstrap method for the two-step estimator of Francq and Zakoïan (2015) associated with the conditional Value-at-Risk. The bootstrap's consistency is proven under mild assumptions for a general class of volatility models and bootstrap intervals are constructed for the conditional Value-at-Risk to quantify the uncertainty induced by estimation. A large-scale simulation study is conducted revealing that the equal-tailed percentile interval based on the fixed-design residual bootstrap tends to fall short of its nominal value. In contrast, the reversed-tails interval based on the fixed-design residual bootstrap yields accurate coverage. In the simulation study we also consider the recursive-design bootstrap. It turns out that the recursive-design and the fixed-design bootstrap perform equally well in terms of average coverage. Yet in smaller samples the fixed-design scheme leads on average to shorter intervals. An empirical application illustrates the interval estimation using the fixed-design residual bootstrap.
Original languageEnglish
Publication statusPublished - 28 Aug 2018

Publication series

SeriesarXiv e-prints
Number1808.09125

JEL classifications

  • c14 - Semiparametric and Nonparametric Methods: General
  • c15 - Statistical Simulation Methods: General
  • c58 - Financial Econometrics

Keywords

  • Residual bootstrap
  • Value-at-Risk
  • GARCH

Cite this

Beutner, E., Heinemann, A., & Smeekes, S. (2018). A Residual Bootstrap for Conditional Value-at-Risk. arXiv e-prints, No. 1808.09125 https://arxiv.org/abs/1808.09125