A residual bootstrap for conditional Value-at-Risk

A fixed-design residual bootstrap method is proposed for the two-step estimator of Francq and Zakoian(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 recursivedesign 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.

Automated summary

This paper proposes a fixed-design residual bootstrap method for the two-step estimator associated with the conditional Value-at-Risk. The consistency of the bootstrap is proven for a general class of volatility models, and intervals are constructed for the conditional Value-at-Risk. Simulation results show that the reversed-tails bootstrap interval provides accurate coverage compared to the equal-tailed percentile bootstrap interval.