A Residual Bootstrap for Conditional Value-at-Risk

TL;DR

This paper introduces a fixed-design residual bootstrap method for estimating the conditional Value-at-Risk, demonstrating its consistency and comparing its performance with recursive bootstrap in simulations and empirical data.

Contribution

It proposes a novel fixed-design residual bootstrap approach for conditional VaR estimation and provides theoretical and empirical validation of its effectiveness.

Findings

Reversed-tails bootstrap intervals achieve accurate coverage.

Fixed-design bootstrap performs well in simulations, with shorter intervals in small samples.

The method is validated through empirical application.

Abstract

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.