### 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 language | English |
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Publication status | Published - 28 Aug 2018 |

### Publication series

Series | arXiv e-prints |
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Number | 1808.09125 |

### 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