Forecasting risk measures using intraday data in a generalized autoregressive score framework

Does safe haven exist? Tail risks of commodity markets during COVID-19 pandemic

“…To investigate the tail riskiness of commodity assets, we rely on the dynamic joint models of VaR and ES introduced by Patton et al (2019) . The vital novelty in their framework is the use of a scaled score to drive the time variation in the target parameter (see, Lazar and Xue, 2020 , for a discussion). It, therefore, can be estimated by minimizing the loss function of Fissler and Ziegel (2016) , namely : where is the asset returns at time , is the probability level for the tail loss distribution, as per Patton et al (2019) , and are the values of VaR and ES, respectively, and is an indicator function which returns when and 0 otherwise.…”

“…But subadditivity is a necessary condition ensuring that the diversification principle of modern portfolio theory holds ( Danielsson et al, 2005 ; Roccioletti, 2016 ). On one side, the past studies have mostly employed the tail risk of VaR, which ignores the shape and structure of the tail and is not a sub-additive risk measure ( Artzner et al, 1997 , 1999 ; Lazar and Xue, 2020 ). On the other side, fewer papers have incorporated estimations of tail risk in commodities through ES modelling (see, for example, Feng et al, 2018 ; Kwon, 2020 ; Mehlitz and Auer, 2021 ; Reboredo, 2013 ; Stavroyiannis, 2018 ).…”

Bootstrapping Time-Varying Uncertainty Intervals for Extreme Daily Return Periods

“…The analysis of Le (2020) advocates asymmetric conditional quantiles and the use of asymmetric Laplace density to jointly estimate value-at-risk and expected shortfall. Additionally, Lazar and Xue (2019) used a new framework for a joint estimation and forecasting the dynamics of VaR and ES. The authors incorporated an intra-day information into a GAS model in order to estimate the risk measures in a quantile regression set-up.…”

Realized Quantiles*

“…For the sake of comparison, we also implement the standard clock-time sampling scheme that samples prices equidistantly in time. We use four frequencies to sample the intraday returns, namely 1-, 3-, 5-, and 10-min. We evaluate and compare the accuracy of our daily VaR and ES forecasts against a battery of models, including standard location-scale models, the approaches of Hallam and Olmo (2014a) and Hallam and Olmo (2014b) and the dynamic VaR and ES models of Patton, Ziegel, and Chen (2019), Taylor (2019), Gerlach and Wang (2019), and Lazar and Xue (2020). We show that our approach significantly outperforms all alternatives, whereas it exhibits the best results when sampling the intraday data at high frequencies and in intrinsic time.…”