A simple empirical inquiry concerning tail risk
Abstract
This research study aims to compare and evaluate the performance of Hill's tail index estimator and the estimator proposed in [1]. The analysis was performed on GARCH (1,1) data which are widely used for modeling processes with time-varying volatility. These include financial time series, which can be particularly heavy-tailed.
The tail index is a key parameter for quantifying the extreme tail behavior of financial time series, which is crucial for risk management and decision-making. The work is an empirical continuation of the results obtained in [12] and it tracks the behavior of the tail index estimators in the simulated GARCH (1,1) samples and also in the case of the GBP/CAD exchange rate between 1st May 2007 and 18th October 2010. The results highlight the strengths and limitations of each estimator and thus provide the possibility of certain improvements to the risk assessment and decision-making processes in various financial applications.
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