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Options Valuation: The Discrete case
Šiklová, Renata ; Zahradník, Petr (advisor) ; Dostál, Petr (referee)
In this work we will get familiarized with a discrete valuation of options. A power- ful and widely applicable numerical method known as the binomial model will be established. Starting with a basic economic idea of non-arbitrage principle we build a risk-neutral world and develop the binomial model for call options. The general binomial model is extended into a trinomial model and there are several parame- terizations that are actually used in practice, provided for both of them. Great emphasis is also focused on a theoretical background. The theoretical knowledge, that will be introduced here in the discrete world, one can regard as basis for con- tinues models. The consequences of probability theory and risk-neutral valuation appear in the valuation of American options. There are three ultimate goals of this work: construction of the model itself, its implementation and an overview of the theoretical background. 1
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Multivariate extreme value theory
Šiklová, Renata ; Mazurová, Lucie (advisor) ; Omelka, Marek (referee)
In this thesis we will elaborate on multivariate extreme value modelling, re- lated practical and theoretical aspects. We will mainly focus on the dependence models, the extreme value copulas in particular. Extreme value copulas effec- tively unify the univariate extreme value theory and the copula framework itself in a single view. We familiarize ourselves with both of them in the first two chapters. Those chapters present generalized extreme value distribution, gen- eralized Pareto distribution and Archimedean copulas, that are suitable for the multivariate maxima and the threshold exceedances description. These two top- ics will be addressed in the third chapter in detail. Taking into consideration rather practical focus of this thesis, we examine the methods of data analysis extensively. Furthermore, we will employ these methods in a comprehensive case study, that will aim to reveal the importance of extreme value theory application in the Catastrophe Insurance. 1
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Multivariate extreme value theory
Šiklová, Renata ; Mazurová, Lucie (advisor) ; Omelka, Marek (referee)
In this thesis we will elaborate on multivariate extreme value modelling, re- lated practical and theoretical aspects. We will mainly focus on the dependence models, the extreme value copulas in particular. Extreme value copulas effec- tively unify the univariate extreme value theory and the copula framework itself in a single view. We familiarize ourselves with both of them in the first two chapters. Those chapters present generalized extreme value distribution, gen- eralized Pareto distribution and Archimedean copulas, that are suitable for the multivariate maxima and the threshold exceedances description. These two top- ics will be addressed in the third chapter in detail. Taking into consideration rather practical focus of this thesis, we examine the methods of data analysis extensively. Furthermore, we will employ these methods in a comprehensive case study, that will aim to reveal the importance of extreme value theory application in the Catastrophe Insurance. 1
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Options Valuation: The Discrete case
Šiklová, Renata ; Zahradník, Petr (advisor) ; Dostál, Petr (referee)
In this work we will get familiarized with a discrete valuation of options. A power- ful and widely applicable numerical method known as the binomial model will be established. Starting with a basic economic idea of non-arbitrage principle we build a risk-neutral world and develop the binomial model for call options. The general binomial model is extended into a trinomial model and there are several parame- terizations that are actually used in practice, provided for both of them. Great emphasis is also focused on a theoretical background. The theoretical knowledge, that will be introduced here in the discrete world, one can regard as basis for con- tinues models. The consequences of probability theory and risk-neutral valuation appear in the valuation of American options. There are three ultimate goals of this work: construction of the model itself, its implementation and an overview of the theoretical background. 1
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