报告地点：行健楼学术活动室526
Abstract: Extreme risk plays an important role in the financial market, which can cause substantial loss in financial investment. To better manage the severe risks resulting from extreme events, we propose a novel fixed-$k$ autoregressive conditional Fréchet ($k$-AcF) model. The proposed model incorporates the $k$-dimensional extreme value distribution and an observation-driven evolution scheme for the key parameters, which accommodates well with the time-varying tail behavior of financial data. Compared to the existing dynamic methods under the extreme value theory framework that focus solely on maximum observations, the $k$-AcF model employs the largest $k$ observations, which enhances the utilization of tail information and obtains a more accurate extreme risk estimation. Furthermore, this paper uses the maximum likelihood estimators to conduct the model estimation and investigates their statistical properties. Simulation studies validate the reliability of the estimators and confirm the theoretical properties of $k$-AcF. Empirical applications to the constituent stocks of two major stock indices of the U.S. demonstrate that the $k$-AcF model sensitively captures the clustering and dynamics of extreme risk in the stock market. Moreover, the results show that our model is more responsive and sensitive to a financial crisis than the benchmark model considering only the maximum observations.
