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Analýza struktury obyvatelstva kraje Vysočina
Slámová, Lenka
The subject of the bachelor's study is to make an analysis of the structure of the inhabitants for region Vysočina in years 2003 to 2013. During this observed period the following demographic indicators were analysed: number of the population, gender, age, education, family state, religion and economic activity. The future progress to the year 2016 was predicted for some indicators. The prognosis was made with the method of balancing of time lines through the appropriate trend function. On the basis of the analysis done was found, that there is a gradual decrease in the number of the inhabitants in region Vysočina. The post-reproduction component has still a bigger representation in the population than pre-reproduction component and thus it comes up to the aging of the population. In total women have a higher representation than men in Vysočina. Further it arises from the analysis, that there is an increase in the number of the people with higher finished graduation, divorced and unemployed people.
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Interest rate options and their valuation in binomial model
Ondruš, Martin ; Slámová, Lenka (advisor) ; Hurt, Jan (referee)
This work discusses about binomial pricing model, which is the basic principle for pricing of any kind of financial assets. We define its brief definition and show its main characteristics. Next, this work discusses about models of the short rate, especially to their discrete versions. From this set of models, we choose one of the most important interest rate models, which is Ho-Lee model and we look at it in details. According to its basis we interpret calibrating of binomial tree. Finally, we perform how to price different kinds of interest rate options such as caps or barrier options according to Ho-Lee model as well. We use mathematical software Mathematica for pricing options and calibrating of binomial tree.
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Modelování úrokových sazeb s využitím Lévyho procesů
Slámová, Lenka ; Beneš, Viktor (advisor) ; Maslowski, Bohdan (referee)
In this work we study the HJM model of the term structure of interest rates driven by a Lévy process. We study the no-arbitrage dynamics of the discounted bond prices and obtain a risk-neutral dynamics of the short rate as a consequence. We study in particular the short rate process and formulate a criteria for mean reversion. The theory gives us a machinery producing short rate processes associated with a general Lévy driver and general volatility structure and we show the non-emptiness of the theory by demonstrating the previous on an example of an OU type process associated with the generalized inverse Gaussian distribution. The upshot is an explicitely given short rate process that generalizes the Vašíček model, and moreover stays positive. Finally we study numerical methods for thus constructed short rate process such as simulations and lattice approximations.
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Near integrated AR(1) models
Onderko, Martin ; Prášková, Zuzana (advisor) ; Slámová, Lenka (referee)
My final thesis firstly addresses basic knowledge of the theory of stochastic processes. This is firstly due to the author's effort to make the thesis more comprehensible, and also due to the need for introduction of key concepts. The autoregressive model AR(1) is defined in the thesis through basic linear time series models, and in this model, the estimation of model parameter by the method of least squares is introduced. For this estimation, the theoretical findings of the thesis are extended through the classical limit theory. Furthermore, the models with their parameter dependent on number of observations are introduced and models of NIAR (1) are defined. Classical limit theory for least squares estimation is then enriched by the limit theory in these models. The category of more general models is introduced and using the acquired knowledge, the features for the model AR (1) are derived. This thesis deals with this issue in models of NIAR (1) and its area of interest is also the bootstrap. The theoretical part of the thesis is supplemented by a practical part represented by numerical studies.
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Generalized stable distributions and their applications
Slámová, Lenka ; Klebanov, Lev (advisor) ; Maslowski, Bohdan (referee) ; Korolev, Victor (referee)
Title: Generalized stable distributions and their applications Author: Mgr. Lenka Slámová, MSc. Department: Department of probability and mathematical statistics Supervisor: Prof. Lev Klebanov, DrSc. Abstract: This thesis deals with different generalizations of the strict stability property with a particular focus on discrete distributions possessing some form of stability property. Three possible definitions of discrete stability are introduced, followed by a study of some particular cases of discrete stable distributions and their properties. The random normalization used in the definition of discrete stability is applicable for continuous random variables as well. A new concept of casual stability is introduced by replacing classical normalization in the definition of stability by random normalization. Examples of casual stable distributions, both discrete and continuous, are given. Discrete stable distributions can be applied in discrete models that exhibit heavy tails. Applications of discrete stable distributions on rating of scientific work and financial time series modelling are presented. A method of parameter estimation for discrete stable family is also introduced. Keywords: discrete stable distribution, casual stability, discrete approximation of stable distribution
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Interest rate options and their valuation in binomial model
Ondruš, Martin ; Slámová, Lenka (advisor) ; Hurt, Jan (referee)
This work discusses about binomial pricing model, which is the basic principle for pricing of any kind of financial assets. We define its brief definition and show its main characteristics. Next, this work discusses about models of the short rate, especially to their discrete versions. From this set of models, we choose one of the most important interest rate models, which is Ho-Lee model and we look at it in details. According to its basis we interpret calibrating of binomial tree. Finally, we perform how to price different kinds of interest rate options such as caps or barrier options according to Ho-Lee model as well. We use mathematical software Mathematica for pricing options and calibrating of binomial tree.
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Modelování úrokových sazeb s využitím Lévyho procesů
Slámová, Lenka ; Maslowski, Bohdan (referee) ; Beneš, Viktor (advisor)
In this work we study the HJM model of the term structure of interest rates driven by a Lévy process. We study the no-arbitrage dynamics of the discounted bond prices and obtain a risk-neutral dynamics of the short rate as a consequence. We study in particular the short rate process and formulate a criteria for mean reversion. The theory gives us a machinery producing short rate processes associated with a general Lévy driver and general volatility structure and we show the non-emptiness of the theory by demonstrating the previous on an example of an OU type process associated with the generalized inverse Gaussian distribution. The upshot is an explicitely given short rate process that generalizes the Vašíček model, and moreover stays positive. Finally we study numerical methods for thus constructed short rate process such as simulations and lattice approximations.
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Analýza struktury obyvatelstva kraje Vysočina
Slámová, Lenka
The subject of the bachelor's study is to make an analysis of the structure of the inhabitants for region Vysočina in years 2003 to 2013. During this observed period the following demographic indicators were analysed: number of the population, gender, age, education, family state, religion and economic activity. The future progress to the year 2016 was predicted for some indicators. The prognosis was made with the method of balancing of time lines through the appropriate trend function. On the basis of the analysis done was found, that there is a gradual decrease in the number of the inhabitants in region Vysočina. The post-reproduction component has still a bigger representation in the population than pre-reproduction component and thus it comes up to the aging of the population. In total women have a higher representation than men in Vysočina. Further it arises from the analysis, that there is an increase in the number of the people with higher finished graduation, divorced and unemployed people.
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