Measuring Tail Thickness Under GARCH and an Application to Extreme Exchange Rate Changes

Abstract

Accurate modeling of extreme price changes is vital to financial risk management. We examine the small sample properties of adaptive tail index estimators under the class of student-t marginal distribution functions including GARCH and propose a model-based bias-corrected estimation approach. Our simulation results indicate that bias strongly relates to the underlying model and may be positively as well as negatively signed. The empirical study of daily exchange rate changes reveals substantial differences in measured tail-thickness due to small sample bias. As a consequence, high quantile estimation may lead to a substantial underestimation of tail risk.

Keywords: fat tails, tail index, stationary marginal distribution, GARCH, Hill estimator, foreign exchange

JEL Classification: C13, C14, F31