Title: A residual bootstrap for conditional value-at-risk
Authors: Alexander Heinemann - Maastricht University (Netherlands) [presenting]
Eric Beutner - Vrije Universiteit Amsterdam (Netherlands)
Stephan Smeekes - Maastricht University (Netherlands)
Abstract: A fixed-design residual bootstrap method is proposed for the two-step estimator associated with the conditional Value-at-risk (VaR). The bootstrap's consistency is proven under mild assumptions for a general class of volatility models and bootstrap intervals are constructed for the conditional VaR 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 on 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.