Title: A novel GARCH-EVT approach dealing with bias and heteroscedasticity for extreme risk estimations
Authors: Hibiki Kaibuchi - SOKENDAI The Graduate University of Advanced Studies (Japan) [presenting]
Gilles Stupfler - ENSAI - CREST (France)
Yoshinori Kawasaki - The Institute of Statistical Mathematics (Japan)
Abstract: Extreme Value Theory (EVT) has not yet emerged as a dominating tool in financial risk management, i.e. extreme risk estimations. This is due to the time-varying volatility of financial time series. In order to overcome this problem, the two-step GARCH-EVT approach was introduced. It should be noted that one drawback of this methodology is that the correction of bias is not thoroughly considered. We propose a new way, as far as we aware, to estimate conditional VaR considering both bias correction and volatility background based on original GARCH-EVT approach. For that, we: (i) pre-whiten the financial time series with a GARCH(1,1) model for forecasting volatility; (ii) apply the semi-parametric bias-corrected tail estimators to standardized residuals from the GARCH analysis. We also consider the extension of extreme expectile estimation to a time dynamic setting. The results are illustrated on simulated data and on a financial real dataset.