Forecasting tail risk of skewed financial returns havingexponential-polynomial tails

Abstract

Aggregated long and short trading risk positions of speculative assets over timeare likely to be unequal. This may be because of irrational decisions of tradersand investors as well as catastrophic events that lead to pronounce or salientmarket crashes. Returns of such assets are therefore more likely to have onepolynomial tail and one exponential tail. The generalized hyperbolic(GH) skewed Student-t distribution is known to handle such situations quitewell. In this paper, we use generalized autoregressive conditional heterosce-dasticity (GARCH) models to empirically show the superiority of the GHskewed Student-t distribution in forecasting the extreme tail risks of cryptocur-rency returns in the presence of substantial skewness in comparison with somecompeting distributions. Furthermore, we show the practical significance ofthe GH skewed Student-t distribution-based risk forecasts in computing dailycapital requirements. Evidence from the study suggests that the GH skewedStudent-t distribution model tends to be superior in forecasting volatility andexpected shortfall (ES) but not value-at-risk. In addition, the distribution yieldshigher value-at-risk (VaR) exceptions but surprisingly avoids the red zone ofthe Basel II accord penalty zones and produces lower but optimal daily capitalrequirements. Therefore, in the presence of substantially skewed returns hav-ing exponential-polynomial tails, we recommend the use of the GH skewedStudent-t distribution for parametric GARCH models in forecasting extremetail risk.