ATM: Autoregressive Tail-index Model for Maxima in Financial Time Series (Zhengjun Zhang, University of Wisconsin-Madison)

Abstract: Classical generalized extreme value (GEV) models have been widely used in the practice of financial risk management for the modeling of extreme observations such as intra-day maximum loss from high-frequency trading or maximum daily loss across a large number of assets in a given portfolio. However, due to the time dependency of financial time series, the classical GEV model, as a static model, cannot fulfill the task of adequately modeling the time-varying behavior of extreme observations. In this paper we integrate the classical GEV with dynamic modeling approach to introduce a novel dynamic GEV framework. Specifically, an autoregressive tail-index model (ATM) is proposed to capture the time-varying tail risk of financial market. Probabilistic properties of the model are studied and an irregular maximum likelihood estimator is used for model estimation, with its asymptotic properties investigated. Finite sample performance is illustrated by simulations. The results of two real data examples in which ATM is used for market tail risk monitoring and VaR calculation are presented, where significant improvement over classical GEV has been observed.