A Residual Bootstrap for Conditional Value-at-Risk

A fixed-design residual bootstrap method is proposed for the two-step estimator of Francq and Zako\"ian (2015) associated with the conditional Value-at-Risk. The bootstrap's consistency is proven for a general class of volatility models and intervals are constructed for the conditional Val...

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Bibliographic Details
Published inarXiv.org
Main Authors Beutner, Eric, Heinemann, Alexander, Smeekes, Stephan
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.08.2023
Subjects
Bootstrap method
Computer simulation
Intervals
Risk levels
Statistical methods
Volatility
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Summary:A fixed-design residual bootstrap method is proposed for the two-step estimator of Francq and Zako\"ian (2015) associated with the conditional Value-at-Risk. The bootstrap's consistency is proven for a general class of volatility models and intervals are constructed for the conditional Value-at-Risk. A simulation study reveals that the equal-tailed percentile bootstrap interval tends to fall short of its nominal value. In contrast, the reversed-tails bootstrap interval yields accurate coverage. We also compare the theoretically analyzed fixed-design bootstrap with the recursive-design bootstrap. It turns out that the fixed-design bootstrap performs equally well in terms of average coverage, yet leads on average to shorter intervals in smaller samples. An empirical application illustrates the interval estimation.
ISSN:2331-8422