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Jingqi Pan (ICMA) “On the estimation of Value-at-risk and Expected Shortfall at extreme levels” – PhD Seminar
The estimation of risk at extreme levels of significance (such as alpha = 0.01%) can be crucial considering events such as those related to the recent COVID-19 crisis. We extend two popular dynamic semi-parametric models of Patton (2019) that jointly estimate Value-at-Risk (VaR) and Expected Shortfall (ES), specifically the one-factor GAS model and the Hybrid GAS/GARCH model. The main idea of our approach is to estimate VaR and ES for two levels of alpha simultaneously, namely for an extreme level and for a more common level (such as 10%). Our simulation results indicate that the proposed models outperform the benchmarks in terms of in-sample loss values, out-of-sample loss and backtest rejections for extreme values of alpha. In an empirical study, we apply the proposed augmented GAS model and the augmented Hybrid GAS/GARCH model to energy futures prices (WTI, Brent, Gas oil and Heating oil) and compare them with a range of parametric, nonparametric and semiparametric models. Our results show that both augmented GAS models generally outperform the benchmark models, and the outperformance is even more prominent during the COVID-19 crisis.