A Residual Bootstrap for Conditional Value-at-Risk

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

Keywords

  • Residual bootstrap
  • Value-at-Risk
  • GARCH

Cite this

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title = "A Residual Bootstrap for Conditional Value-at-Risk",
abstract = "This paper proposes a fixed-design residual bootstrap method for the two-step estimator of Francq and Zako{\"i}an (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.",
keywords = "Residual bootstrap, Value-at-Risk, GARCH",
author = "Eric Beutner and Alexander Heinemann and Stephan Smeekes",
year = "2018",
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language = "English",
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A Residual Bootstrap for Conditional Value-at-Risk. / Beutner, Eric; Heinemann, Alexander; Smeekes, Stephan.

2018.

Research output: Working paperProfessional

TY - UNPB

T1 - A Residual Bootstrap for Conditional Value-at-Risk

AU - Beutner, Eric

AU - Heinemann, Alexander

AU - Smeekes, Stephan

PY - 2018/8/28

Y1 - 2018/8/28

N2 - 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.

AB - 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.

KW - Residual bootstrap

KW - Value-at-Risk

KW - GARCH

M3 - Working paper

BT - A Residual Bootstrap for Conditional Value-at-Risk

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