Work detail

Estimation and Application of the Tail Index

Author: Bc. Markéta Pokorná
Year: 2016 - summer
Work type: Bachelors
Language: English
Pages: 81
Awards and prizes:
Abstract: Examining the nature of extreme values plays an important role in financial
risk management. This thesis investigates tail behaviour of distribution of returns
using the framework of univariate Extreme Value Theory. The empirical
research was conducted on the S&P 500 index and its seven constituents. The
goal of this thesis was to use the Hill method to estimate the tail index of the
series which characterizes the tail behaviour, especially the speed of the tail
decay. To select the tail threshold several graphical methods were performed
as they represent empirical measures of model stability. Classical Hill plots as
well as alternative Hill plots and smoothing procedure were presented. The
threshold choice based on stable regions in the graphs was found to be highly
subjective. Hill method modified by Huisman was used instead and the results
confirmed that the classical Hill method yields estimates which overestimate
the tail thickness. All the examined series were found to have heavy tails with
polynomial tail decay. This thesis stressed the need to model the left and the
right tail separately as both extreme losses and profits are important depending
on whether an investor takes a long or a short position on portfolio. Finally, the
tail index was used to demonstrate the need to compute the expected losses for
certain quantiles instead of simply the minimum losses as expressed by Value
at Risk.


Česká Spořitelna


Patria Finance