Most suitable threshold method for extremes in financial data with different volatility levels

¹ Department of Actuarial Science, Faculty of Commerce, University of Cape Town, South Africa
² Department of Mathematical Statistics and Actuarial Science, Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa

^* Corresponding author: shongwesc@ufs.ac.za

Abstract

Estimating the threshold for extreme values is essential for anticipating and managing rare and impactful events. This paper discusses four different graphical methods of estimating thresholds using three different stock price datasets. The datasets have different levels of volatility (classified as low, medium, and high). For each of the datasets, thresholds are estimated, and a generalised Pareto distribution is then fitted to the exceedances above each threshold. Subsequently, the mean squared error is calculated for each fitted model, which is then used together with the number of exceedances for each respective threshold as criteria to analyse and make inferences on the most suitable threshold approach when using a dataset that has a specified degree of volatility. It was observed that when dealing with a dataset with low volatility, Pickand plot should be considered for threshold setting. When volatility is very moderate or high, using Hill plot to determine thresholds for extreme values is recommended. The motivation for this paper lies in the need to explore and identify the most effective threshold estimation methods when dealing with different levels of stock price volatility.