Master's Thesis Presentation
Department of Statistics
The University of Chicago
"On two-step estimation of extreme VaR: would incorporating realized measures and bias-adjusted extreme value index estimation boost accuracy?"
Monday, November 27th, 2023, at 2:00 PM
Jones 111, 5747 S. Ellis Avenue
The Value-at-Risk (VaR), introduced by JPMorgan in 1993, is a widely employed instrument to capital allocation and risk management. To account for the conditional heteroskedasticity observed in series of stock prices, GARCH-type filtering is commonly used to predict the mean and implicit volatility of these series; since the return is usually heavy-tailed, extreme value theory is popular in modeling the innovations. In this study, four different two-step forecast procedures of the one-step-ahead extreme VaR were compared, with either standard-GARCH or realized-GARCH combined with either normal innovations or extreme value index under the unbiased Gomes-de Hann (UGH) approach. In particular, the realized-GARCH-UGH is a novel model proposed and tested in this study. The results indicate that for stock indices, the UGH method is better than assuming normal innovations; the realized-GARCH-UGH has similar performance to standard-GARCH-UGH. However, the forecast using the realized-GARCH-UGH on Bitstamp, a cybercurrency, has a severe over coverage. Rick managers can choose the filtering method based on backtesting results.