Forecasting tail risk of skewed financial returns having exponential-polynomial tails

Abstract

Aggregated long and short trading risk positions of speculative assets over time are likely to be unequal. This may be because of irrational decisions of traders and investors as well as catastrophic events that lead to pronounce or salient market crashes. Returns of such assets are therefore more likely to have one polynomial tail and one exponential tail. The generalized hyperbolic (GH) skewed Student-t distribution is known to handle such situations quite well. In this paper, we use generalized autoregressive conditional heteroscedasticity (GARCH) models to empirically show the superiority of the GH skewed Student-t distribution in forecasting the extreme tail risks of cryptocurrency returns in the presence of substantial skewness in comparison with some competing distributions. Furthermore, we show the practical significance of the GH skewed Student-t distribution-based risk forecasts in computing daily capital requirements. Evidence from the study suggests that the GH skewed Student-t distribution model tends to be superior in forecasting volatility and expected shortfall (ES) but not value-at-risk. In addition, the distribution yields higher value-at-risk (VaR) exceptions but surprisingly avoids the red zone of the Basel II accord penalty zones and produces lower but optimal daily capital requirements. Therefore, in the presence of substantially skewed returns having exponential-polynomial tails, we recommend the use of the GH skewed Student-t distribution for parametric GARCH models in forecasting extreme tail risk.