<p>Extreme risk plays an important role in financial supervision and financial investment, which can cause substantial loss in the financial market. To better manage the severe risks resulting from extreme events, the authors propose a novel fixed-<i>k</i> autoregressive conditional Fréchet (<i>k</i>-AcF) model. The proposed model incorporates the <i>k</i>-dimensional extremal 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 <i>k</i>-AcF model employs the largest <i>k</i> 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 <i>k</i>-AcF. Empirical applications to the constituent stocks of two major stock indices in the U.S. demonstrate that the <i>k</i>-AcF model accurately captures the clustering and dynamics of extreme risk in the stock market. Moreover, the results show that the obtained model is more responsive and sensitive to a financial crisis than the benchmark model considering only the maximum observations.</p>