An Application of Extreme Value Theory for Financiel Risk Management

Christoffer R. Hansen

Student thesis: Master thesis

Abstract

The purpose of this dissertation is to investigate the estimation process of financial risk measures and whether different methods can help optimize the estimates and give a better reflection of the risks related to a financial asset. The focus is on Extreme Value Theory (EVT) and its possible benefits when estimating risk for financial time series, and the methods chosen are the Block Maxima- and Peaks Over Threshold methods. Different methods is proposed, including a combined GARCH-EVT model for modelling the variance structure of a process, for estimating Value-at-Risk (VaR) and Expected Shortfall (ES). In order to correctly apply the methods and estimate Value-at-Risk and Expected Shortfall, relevant theory of Extreme Value Theory, financial risk measures and heteroscedastic models is described. The theory is then applied in practice to three historical daily return series, the stock of Danske Bank A/S, Vestas Wind Systems A/S and A.P. Moeller – Maersk A/S (B stock), in an attempt to evaluate the risk measures, Value-at-Risk and Expected Shortfall, for different methods. A combined model of GARCH-EVT using Peaks Over Threshold to identify extreme values proved to result in higher risk estimates compared to the simple GARCH- and EVT models as well as the GARCH-EVT model using the Block Maxima method, indicating that methods which ignore tail risk or volatility structure tend to underestimate the financial risk of an asset.

EducationsMSc in Business Administration and Mathematical Business Economics, (Graduate Programme) Final Thesis
LanguageDanish
Publication date2021
Number of pages104
SupervisorsDorte Kronborg