An empirical analysis of tail risk forecasting using realized quantiles

Abstract

Traditional risk measures based on daily returns fail to capture the complex tail dynamics of modern financial markets. This thesis reimplements and validates the realized quantile framework of Halbleib and Dimitriadis (2022) using independent high-frequency data covering 55 U.S. stocks from 2009 to 2019. We compare intrinsic-time sampling schemes which include business time sampling, trade time sampling, and tick time sampling, against conventional constant-time approaches to forecast value at risk and expected shortfall. Our out-of-sample evaluation demonstrates that intrinsic-time sampling significantly outperforms calendar-time methods at extreme tails (99\% VaR), with business time sampling achieving better performance. At intermediate quantiles (95-97.5\% VaR), activity-based schemes dominate, highlighting that different tail regions require different sampling approaches. The results validate the framework's robustness across an independent implementation and different and larger set of stocks. All code is released as open-source to support reproducible research in financial econometrics.