This bachelor thesis studies and practices the employment of the extreme value theory (EVT) into risk management, as a method of modeling and assessing the extreme risks. Without loss of generality, a sequence of procedures utilizing the peaks over threshold (POT) model in stress-testing of the market risks is performed. Risk management is concerned with the identification, assessment and prioritization of various risks, so as to minimize and control the probability or impact of unfavorable events. Since years, the operation reforms from subjective recognition by leadership fellows, to risk quantification through statistical models. Specifically, the EVT has been studied and applied widely in dealing with low probability high consequence events, which usually possess the character of a fat-tailed distribution pattern.
Thus, the practice of tail-fitting approach of the EVT is of great importance. Hereby, the POT approach, based on modeling excess values of a sample set over a threshold within a time period, is focused on and it provides a straightforward tool for estimating measures of tail risks at high quantiles. Generalized Pareto distribution (GPD) is used to approximate the distribution of excess amounts over sufficiently high thresholds. The thresholds are optimized through the combined graphic approaches of the ME-plot and the Hill-plot. Both methods are conducted to estimate the parameters for the GPD. With the aid of parameter assessment methods and criteria, parameter pairs with appropriate quality can be determined.
This procedure is performed and used in stress-testing of the market risks in the Investionsbank Berlin (IBB). The risk-free interest rate premium for each quantile is thereupon acquired for the stress-testing. The results imply that the POT method performs effectively for the stress-testing.
Peaks over Threshold method, generalized Pareto distribution