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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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Solvency II: solvency in insurance
Čáha, Pavel ; Cipra, Tomáš (advisor) ; Mazurová, Lucie (referee)
This thesis is dedicated to Solvency II, a regulatory framework for insurance and reinsurance companies effective in European Union. Firstly, it explains the notion solvency and also describes the principles of the regulation itself. Another part is focused on the calculation of solvency capital requirement and minimal capital requirement, using standard formula. The capital requirements are derived on the level of risk modules and their submodules. Furthermore, the topic of technical reserves is discussed and emphasis is placed on the derivation of mean square error of prediction. Described methods are Chain-Ladder and Bornhuetter-Ferguson. The last part of the thesis includes the calculation of capital requirements for real data. A program SolvencyII.xlsx that shows particular derivations is enclosed.
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Tweedie models for pricing and reserving
Smolárová, Tereza ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
This presented thesis deals with applications of Tweedie compound Poisson model in non-life insurance pricing and claims reserving. Tweedie models are exponen- tial dispersion models with power mean-variance relationships and compound Poisson distribution is a particular Tweedie model. The interest in Tweedie com- pound Poisson model is motivated by its applications to generalized linear models (GLMs) and generalized estimation equations (GEE). The purpose of this thesis is to construct pricing and claims reserving models in which the response variables follow Tweedie compound Poisson model. Theoretical approaches are applied on the real datasets. 1
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Projection of mortality tables and their influence on insurance embedded value
Filka, Jakub ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
We study development of mortality tables from 1950 to present in Czech Republic. Our aim is to look at the 6 basic models, which can be potentially used to describe behavior of dying for people over 60 years. Models that are being investigated vary from generally accepted Gompertz-Makeham model to logistic models of Thatcher and Kannisto. We also introduce Coale-Kisker and Heligman- Pollard model. Our analysis is concentrated mostly on projecting abilities of given models to the highest ages. Especially for women, where data do not show such dispersion as in the case of men, there is a visible trend that can be described better by using logistic models instead of Gompertz-Makeham model, which has a tendency to overestimate the probabilities of dying in higher ages. Keywords: projection of mortality tables, Gompertz-Makeham, logistic models 1
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Stochastic mortality modeling for multiple populations
Skřivanová, Zuzana ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
Title: Stochastic mortality modelling for multiple populations Abstract: This thesis deals with the possibilities of modelling and forecasting of age-specific mortality rates. The introductory part summarizes the basic terms from demo- graphy, which are related to mortality, and specifies elementary approaches to the mortality modelling. Subsequently there are in detail described the three most commonly used stochastic mortality models - Lee-Carter, Renshaw-Haberman and Cairns-Blake-Dowd. The fundamental part of this thesis deals with the possi- bilities of using these models for mortality modelling simultaneously in correlated populations. These theoretical bases are in the final part of this thesis numerically illustrated on the mortality models for populations of Czech and Slovak Republic. 1
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Investment Strategies for Financial Derivatives
Voráčková, Andrea ; Hurt, Jan (advisor) ; Cipra, Tomáš (referee)
This bachelor thesis deals with various methods of valuing options. First, the basic definitions and relations concerning options are introduced. The second part is focused on Black-Scholes and binomial model and the relation between these models is proved. The Cox-Ross-Rubinstein and Jarrow-Rudd methods are introduced as well as the approximate versions of these methods. The numerical part consists of applying aforesaid methods on data using software Mathematica. The strengths and weaknesses of these methods are described and outcomings are compared with thesis of Hull (2012) and Shaw (2002). Powered by TCPDF (www.tcpdf.org)
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Selected problems of financial time series modelling
Hendrych, Radek ; Cipra, Tomáš (advisor) ; Arlt, Josef (referee) ; Prášková, Zuzana (referee)
Title: Selected problems of financial time series modelling Author: Radek Hendrych Department: Department of Probability and Mathematical Statistics (DPMS) Supervisor: Prof. RNDr. Tomáš Cipra, DrSc., DPMS Abstract: The present dissertation thesis deals with selected problems of financial time series analysis. In particular, it focuses on two fundamental aspects of condi- tional heteroscedasticity modelling. The first part of the thesis introduces and discusses self-weighted recursive estimation algorithms for several classic univariate conditional heteroscedasticity models, namely for the ARCH, GARCH, RiskMetrics EWMA, and GJR-GARCH processes. Their numerical capabilities are demonstrated by Monte Carlo experiments and real data examples. The second part of the thesis proposes a novel approach to conditional covariance (correlation) modelling. The suggested modelling technique has been inspired by the essential idea of the multivariate orthogonal GARCH method. It is based on a suitable type of linear time-varying orthogonal transformation, which enables to employ the constant conditional correlation scheme. The correspond- ing model is implemented by using a nonlinear discrete-time state space representation. The proposed approach is compared with other commonly applied models. It demon- strates its...
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Econometric models for Czech insurance market
Vichr, Jaroslav ; Cipra, Tomáš (advisor) ; Pešta, Michal (referee)
Relationships between insurance variables representing the cash flows of the Czech insurance market can be effectively modeled using a dynamic system of linear simultaneous equations. The source of the underlying data to build such a model can be publicly available annual reports of the Czech Insurance Association. The resulting model can find its use mainly to predict the future development of financial flows based on historical observations and analysis of possible scenarios. It is this analysis of potential projections and their consequences which provides insight into how e.g. a future decrease of new insurance policies would affect the expected amount of claims costs and the volume of written premiums.
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Claims reserving within the panel data framework
Gerthofer, Michal ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
In the presented thesis the issue of dependency between response variables within the subjects in the generalized linear models framework is investigated. Reserving in non-life insurance is a key factor for the financial position of a company. The text introduces the basic actuarial notation, terminology and methods. The main part is focused on panel data framework, especially Generalized Linear Mixed Models (GLMM) as well as Generalized Estimating Equations (GEE), and their application on claims reserving. The aim of this thesis is to show the advantages, disadvantages, limitations and the comparison of these approaches on representative datasets, which were chosen according to results obtained from whole database analysis. Significant focus is on model selection and diagnostics used for this purpose. Finally, the obtained results are summarized in tables, figures and the comparison of the methods is provided. Powered by TCPDF (www.tcpdf.org)
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Generalized Leontiev models
Hála, Petr ; Kopa, Miloš (advisor) ; Cipra, Tomáš (referee)
"his thesis de-ls with veontiev¡s input -nd output model of the e onomy -nd its potenti-l extensionsF et the eginning of the thesis -si formul-tions -nd h-r- teristi s of the veontiev¡s model -re summ-rized with emph-sis on its solv- ilityF sn the third -nd fourth h-pterD we present the simplest modi( -tions with -ddition-l restri tions or o je tive fun tionF sn the sixth h-pter - dyn-mi model with dis rete time is derivedD -g-in with emph-sis on the formul-tion of the onditions of existen e of solutionF "he l-st h-pter presents - sto h-sti gener-liz-tion of the veontiev¡s model using pro - ilisti onstr-ints -nd the s en-rio -ppro- hF "he thesis is - omp-nied y its own ex-mple of veontiev¡s sto h-sti modelF
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