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Value-at-Risk Calculation Using Extreme Value Theory
Lipták, Patrik ; Hendrych, Radek (advisor) ; Mazurová, Lucie (referee)
This diploma thesis studies extreme value theory and its application in finan- cial risk management, when focusing on computation of well-known risk measure - Value at Risk (VaR). The first part of the thesis reviews theoretical background. In particular, it rigorously discusses the extreme value theory when emphasi- zing fundamentals theorems and their consequences followed by the summary of methods based on this theory, specifically, Block Maxima method, Hill met- hod and Peaks over Threshold method. Moreover, specific issues that may arise in such applications and ways how to deal with these problems are described. The second part of the thesis contains extensive empirical study, which together with theoretical foundings applies each of the examined method to real market data of the closing prices of Dow Jones Industrial Average stock index, stocks of JPMorgan and stock index Russell 2000 in order to compare methods based on extreme value theory together with the classic methodology RiskMetrics. 1
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Durbin-Watson test
Lipták, Patrik ; Zvára, Karel (advisor) ; Anděl, Jiří (referee)
The Bachelor Thesis deals with Durbin-Watson test which is used to test an inde- pendence of residuals in a normal linear regression model. The test is applicable in a case of collecting data gradually and if values of a dependent variable form time series. In the first part, thesis provides detailed derivation of a distribution of test statistic (or its bounds), as well as conclusion describing how to make a right decision in testing a hypothesis that the value of correlation coefficient is equal to 0. In the second part, three practical examples with real data are used to demonstrate this theoretical basis. Moreover, calculations are supplemented by illustrative graphs and they are made in computing environment R for com- parison. 1
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