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Financial risks with copulas
Prelecová, Natália ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The aim of this thesis is the thorough description of the copula theory. It deals with the theory's basic definitions, classes and characteristics. In addition, relations between copulas and dependence measures are explained. Furthermore, we evaluate the possibilities of copula's parametres estimation and selecting the right copula for real data. Then, the copula theory is interconnected with the basic risk measures in finance. We describe the elementary categorization of financial risks and standard risk measurement approaches. We also define basic risk measures with the emphasis on value at risk. Lastly, we present a real data case study of a selected portfolio.
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Introduction to Nonparametric Methods
Prelecová, Natália ; Kulich, Michal (advisor) ; Navrátil, Radim (referee)
Title: Introduction to Nonparametric Methods Author: Natália Prelecová Department: Department of Probability and Mathematical Statistics Supervisor: doc. Mgr. Michal Kulich,Ph.D., Department of Probability and Mathematical Statistics Abstract: The aim of this thesis is to introduce basic nonparametric methods. Nonparametric methods embrace a large class of statistical procedures which do not assume specific data distribution such as normal distribution. They often re- present the only available means of examining specific types of data, for example ranks or counts. Weaker assumptions of these methods make them less powerful than their parametric counterparts. This thesis describes in detail four nonparametric tests- the Ordinary Sign Test, the Wilcoxon Signed-rank Test, the Mann-Whitney Test and finally the Two- sample Wilcoxon Test. The structure of their description will entail the following: the formulation of assumptions, null hypothesis and alternatives, the construction of the test statistic and the definition of rejection regions. The most essential prob- lems, such as the problem of ties, will be also covered. The basic characteristics of the Linear Rank Statistics will be also explained, followed by the Two-sample Wilcoxon test. Keywords: nonparametrical, hypothesis, ranks, consistency, statistic
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Financial risks with copulas
Prelecová, Natália ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The aim of this thesis is the thorough description of the copula theory. It deals with the theory's basic definitions, classes and characteristics. In addition, relations between copulas and dependence measures are explained. Furthermore, we evaluate the possibilities of copula's parametres estimation and selecting the right copula for real data. Then, the copula theory is interconnected with the basic risk measures in finance. We describe the elementary categorization of financial risks and standard risk measurement approaches. We also define basic risk measures with the emphasis on value at risk. Lastly, we present a real data case study of a selected portfolio.
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Introduction to Nonparametric Methods
Prelecová, Natália ; Kulich, Michal (advisor) ; Navrátil, Radim (referee)
Title: Introduction to Nonparametric Methods Author: Natália Prelecová Department: Department of Probability and Mathematical Statistics Supervisor: doc. Mgr. Michal Kulich,Ph.D., Department of Probability and Mathematical Statistics Abstract: The aim of this thesis is to introduce basic nonparametric methods. Nonparametric methods embrace a large class of statistical procedures which do not assume specific data distribution such as normal distribution. They often re- present the only available means of examining specific types of data, for example ranks or counts. Weaker assumptions of these methods make them less powerful than their parametric counterparts. This thesis describes in detail four nonparametric tests- the Ordinary Sign Test, the Wilcoxon Signed-rank Test, the Mann-Whitney Test and finally the Two- sample Wilcoxon Test. The structure of their description will entail the following: the formulation of assumptions, null hypothesis and alternatives, the construction of the test statistic and the definition of rejection regions. The most essential prob- lems, such as the problem of ties, will be also covered. The basic characteristics of the Linear Rank Statistics will be also explained, followed by the Two-sample Wilcoxon test. Keywords: nonparametrical, hypothesis, ranks, consistency, statistic
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