Linking Tukeys legacy to financial risk measurement
We derive Value at Risk and expected shortfall for GTL-distributed random variables. GTLs VaR and ES statistics differ significantly from other flexible distributions. We derive asymptotic properties of the ML estimator of the GTL parameters. We insert GTL and other flexible distributions in a GARCH model. A GTL-GARCH model may fit real data better than GARCH with other distributions.
value at risk expected shortfall asymptotic properties garch model generalized tukey lambda distribution skewness thick-tailed distribution maximum likelihood estimation risk management