Statistical aspects of Extreme Value Theory with an application in seismic analysis

Open House, ISM in Tachikawa, 2018.6.15統計数理研究所オープンハウス（立川）、H30.6.15ポスター発

Value-at-Risk estimation: A novel GARCH-EVT approach dealing with bias and heteroscedasticity

Open House, ISM in National Center of Sciences Building, 2019.6.05統計数理研究所オープンハウス（学術総合センター）、R1.6.5ポスター発

GARCH-UGH: A bias-reduced approach for dynamic extreme Value-at-Risk estimation in financial time series

ISM Online Open House, 2021.6.18統計数理研究所オープンハウス（オンライン開催）、R3.6.18ポスター発

A bias-reduced GARCH-EVT(Extreme Value Theory) approach for financial risk estimation

ISM Online Open House, 2020.10.27統計数理研究所オープンハウス（オンライン開催）、R2.10.27ポスター発

GARCH-UGH: a bias-reduced approach for dynamic extreme Value-at-Risk estimation in financial time series

The Value-at-Risk (VaR) is a widely used instrument in financial risk management. The question of estimating the VaR of loss return distributions at extreme levels is an important question in financial applications, both from operational and regulatory perspectives; in particular, the dynamic estimation of extreme VaR given the recent past has received substantial attention. We propose here a new two-step bias-reduced estimation methodology for the estimation of one-step ahead dynamic extreme VaR, called GARCH-UGH (Unbiased Gomes-de Haan), whereby financial returns are first filtered using an AR-GARCH model, and then a bias-reduced estimator of extreme quantiles is applied to the standardized residuals. Our results indicate that the GARCH-UGH estimates of the dynamic extreme VaR are more accurate than those obtained either by historical simulation, conventional AR-GARCH filtering with Gaussian or Student-t innovations, or AR-GARCH filtering with standard extreme value estimates, both from the perspective of in-sample and out-of-sample backtestings of historical daily returns on several financial time series