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Modeling of duration between financial transactions
Voráčková, Andrea ; Zichová, Jitka (advisor) ; Pawlas, Zbyněk (referee)
❆❜str❛❝t ❚❤✐s ❞✐♣❧♦♠❛ t❤❡s✐s ❞❡❛❧s ✇✐t❤ ♣r♦♣❡rt✐❡s ♦❢ ❆❈❉ ♣r♦❝❡ss ❛♥❞ ♠❡t❤♦❞s ♦❢ ✐ts ❡st✐♠❛t✐♦♥✳ ❋✐rst✱ t❤❡ ❜❛s✐❝ ❞❡☞♥✐t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ ❆❘▼❆ ❛♥❞ ●❆❘❈❍ ♣r♦❝❡ss❡s ❛r❡ st❛t❡❞✳ ■♥ t❤❡ s❡❝♦♥❞ ♣❛rt ♦❢ t❤❡ t❤❡s✐s✱ t❤❡ ❆❈❉ ♣r♦❝❡ss ✐s ❞❡☞♥❡❞ ❛♥❞ t❤❡ r❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ❆❘▼❆ ❛♥❞ ❆❈❉ ✐s s❤♦✇♥✳ ❚❤❡♥ ✇❡ s❤♦✇ t❤❡ ♠❡t❤♦❞s ♦❢ ❞❛t❛ ❛❞❥✉st♠❡♥t✱ ❡st✐♠❛t✐♦♥✱ ♣r❡❞✐❝t✐♦♥ ❛♥❞ ✈❡r✐☞❝❛t✐♦♥ ♦❢ t❤❡ ❆❈❉ ♠♦❞❡❧✳ ❆❢t❡r t❤❛t✱ t❤❡ ♣❛rt✐❝✉❧❛r ❝❛s❡s ♦❢ ❆❈❉ ♣r♦❝❡ss✿ ❊❆❈❉✱ ❲❆❈❉✱ ●❆❈❉✱ ●❊❱❆❈❉ ✇✐t❤ ✐ts ♣r♦♣❡rt✐❡s ❛♥❞ t❤❡ ♠♦t✐✈❛t✐♦♥❛❧ ❡①❛♠♣❧❡s ❛r❡ ✐♥tr♦❞✉❝❡❞✳ ❚❤❡ ♥✉♠❡r✐❝❛❧ ♣❛rt ✐s ♣❡r❢♦r♠❡❞ ✐♥ ❘ s♦❢t✇❛r❡ ❛♥❞ ❝♦♥❝❡r♥s t❤❡ ♣r❡❝✐s✐♦♥ ♦❢ t❤❡ ❡st✐♠❛t❡s ❛♥❞ ♣r❡❞✐❝t✐♦♥s ♦❢ t❤❡ s♣❡❝✐❛❧ ❝❛s❡s ♦❢ ❆❈❉ ♠♦❞❡❧ ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❧❡♥❣t❤ ♦❢ s❡r✐❡s ❛♥❞ ♥✉♠❜❡r ♦❢ s✐♠✉❧❛t✐♦♥s✳ ■♥ t❤❡ ❧❛st ♣❛rt✱ ✇❡ ❛♣♣❧② t❤❡ ♠❡t❤♦❞s st❛t❡❞ ✐♥ t❤❡♦r❡t✐❝❛❧ ♣❛rt ♦♥ r❡❛❧ ❞❛t❛✳ ❚❤❡ ❛❞❥✉st♠❡♥t ♦❢ t❤❡ ❞❛t❛ ❛♥❞ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ♣❛r❛♠❡t❡rs ✐s ♣❡r❢♦r♠❡❞ ❛s ✇❡❧❧ ❛s t❤❡ ✈❡r✐☞❝❛t✐♦♥ ♦❢ t❤❡ ❆❈❉ ♠♦❞❡❧✳ ❆❢t❡r t❤❛t✱ ✇❡ ♣r❡❞✐❝t ❢❡✇ st❡♣s ❛♥❞ ❝♦♠♣❛r❡ t❤❡♠ ✇✐t❤ r❡❛❧ ❞✉r❛t✐♦♥s✳ ✶
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Aggregate loss models with dependent frequency and severity
Čápová, Petra ; Mazurová, Lucie (advisor) ; Zichová, Jitka (referee)
In non-life insurance, the independence between the number and size of claims is usually assumed. However, this thesis shows that the assumption of independence can be omitted. We deal with the dependency modeling between frequency and severity of claims. For including the dependence to the total claims model, we consider two methods. The first method uses generalized linear models and the second method used in the thesis is based on dependence modeling by copulas. We also perform a model with independent frequency and severity of claims. This model is compared with the described methods in the simulation part of the thesis. We include dependency on explanatory (rating) variables in all of these models. 1
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Autoregressive models
Rathouský, Marek ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
The purpose of this thesis is to compare the classic autoregressive model of order 1 to integer autoregressive model of order 1. Considering the popularity of AR(1) model, only the basics are covered within this thesis. The main focus is on the INAR(1) model. Operator ◦ necessary for INAR(1) definition is intro- duced alongside with its properties with proof. All of the non-trivial properties of INAR(1) are followed by detailed proof, stationarity condition is also derived. Common estimation techniques are described for poisson INAR(1) model. This thesis also contains simulation study, which focuses on the rate of convergence of estimates of parameters. 1
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Cointegration and EC model
Asipenka, Hanna ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
The thesis deals with the concept of cointegration of time series and related error correction model. First, we introduce the basic definitions and theorems that are necessary for understanding the subject of other chapters. Then we focus on the definition of cointegration and the issue of tests for cointegration. Next, we define the error correction model in general in the vector autoregression as well. We will show and prove Granger's representation theorem, which will allow the construction of the EC model in the next section of the chapter. Finally, we apply the written theory to real time series. We perform cointegration tests and construct the relevant EC model. 1
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Multivariate models of volatility
Vejmělka, Petr ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
In this work, we deal with the modeling of multivariate financial time series. First, linear models of multivariate time series are described and further special features of the financial time series. In the next part of the thesis, we focus on modeling multivariate volatility and present several models that can be used in this context. In the practical part of the work, we apply some of these models on real data using the software systems EViews 9 and RATS 8. As the first one, we analyze gradually two-dimensional and five-dimensional financial time series. The aim of thesis is to survey the temporary state of multivariate volatility modeling in financial time series including practical experience with specialized software. 1
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Random rates of return in financial and insurance mathematics
Pejic, Mladen ; Zichová, Jitka (advisor) ; Mazurová, Lucie (referee)
Title: Random rates of return in financial and insurance mathematics Author: Mladen Pejic Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr., Department of Probability and Mathema- tical Statistics Abstract in English language: The thesis is focused on the study of stochastic life annuities. It represents a combination of basic probability with financial mathe- matics and life insurance. The first part is focused on financial mathematics. Special attention is paid to the calculation of present and future values of annui- ties with stochastic interest rates. In the second part, we demonstrate the use of random interest rates in calculations of present values of annuities related to life insurance. In the third part, we focus on the application of log - normal distribu- tion, which is mostly used in real life problems. In the last part, a numerical study is presented. We asses the effect of the log - normal distribution parameters on the present value of the annuities and we examine the accuracy of the estimates made by the method of moments. ii
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LDA approach to operational risk modelling
Kaplanová, Martina ; Mazurová, Lucie (advisor) ; Zichová, Jitka (referee)
In this thesis we will deal with the term of operational risk, as it is presented in the directives Basel 2 that are mandatory for financial institutions in the European Union. The main problem is operational risk modeling, therefore, how to measure and manage it. In the first part we will look at the possibility of calculating the capital requirements for operational risk under Basel 2, mainly the calculation with the internal model. We will describe the specific procedures for the development of the internal model and we will focus on Loss Distribution Approach. The internal model will be based on modeling of loss in each risk cell separately. In the second part we will show, how to include modeling of dependence structure between risk cells to the internal model with using copulas. Finally, we will show the illustrative example, where we will see, whether the modeling of dependence leads to a reduction of the total capital requirement. Powered by TCPDF (www.tcpdf.org)
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Financial time series model identification
Fučík, Jan ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
This thesis deals with the financial time series model identification. The univariate and multivariate ARMA models and their identification criteria are described. The procedures using the correlation structure of the time series and some information criteria are presented. The functioning of the criteria is verified on simulated time series AR, MA and ARMA. Afterwards, the criteria are compared in terms of reliability and simplicity of use. Finally, there are two examples of univariate and multivariate ARMA model identification for the real financial time series. The data and the R programme source code are enclosed on a CD. Powered by TCPDF (www.tcpdf.org)
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Special problems of non-stationarity in financial time series
Radič, Pavol ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
The aim of this thesis is a detailed analysis of selected approaches of unit root testing. First chapter deals with the basic knowledge of the theory of stochastic processes. Further, we describe Dickey-Fuller tests, t-tests and likelihood ratio tests for the presence of a unit root and derive their asymptotic properties. Numerical studies include comparison of accuracy of the parameter estimates, estimating quantiles of the presented distributions, their graphical presentation and determination of power of our tests. The acquired theoretical knowledge is applied on real data which were analyzed using software Mathematica and R. Powered by TCPDF (www.tcpdf.org)
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Treshold models for financial time series
Stacho, Michal ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
In modeling of financial time series is widely accepted ARCH model with conditional heteroscedasticity, but this model is not able to operate with other non-linearities such as leverage or asymmetry (the volume of revenue is different when the yield is positive or negative). Therefore, we work in this thesis with threshold models TAR, TARCH and DTARCH. These models have piecewise linear conditional mean and DTARCH model even piecewise linear conditional variance. The main utility of threshold models is further specified test of threshold nonlinearity, which is the base for comprehensively defined procedure of determining the type of model, including an estimate of all its parameters. At the end, the procedures introduced in this text are demonstrated using simulated and real data. Powered by TCPDF (www.tcpdf.org)
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