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Multivariate volatility models
Šimjáková, Dominika ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The subject of the thesis is the analysis of univariate and multivariate time series. The GARCH models as well as the the simpli cated ARCH models are described in detail. In the practical part of the master thesis are elaborated some time series of exchange rates. The aim of this work is to nd an appropriate model which would reliably aproximate the development of the series. The exchange rates time series were analyzed by the software XploRe and Eviews. The data and programme source code are enclosed on a CD.
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Parametrizace rozdělení škod v neživotním pojištení
Špaková, Mária ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
Title: Parameterization of claims distribution in non-life insurance Author: Bc. Mária Špaková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta Ph.D., MFF UK Abstract: This paper deals with the parameterization of claim size distributions in non-life insurance. It consists of the theoretical and the practical part. In the first part we discuss the usual distributions of claims and their properties. One section is devoted to extreme values distributions. Consequently, we mention the most known methods for parameter estimation - the maximum likelihood method, the method of moments and the method of weighted moments. The last theoretical chapter is focused on some validation techniques and goodness-of-fit tests. In the practical part we apply some of the discussed approaches on real data. However, we concentrate mainly on the large claims modeling - firstly, we select a reasonable threshold for our data and then we fit the claims by the generalized Pareto distribution together with the introduced parameterization procedures. Based on the results of the applied validation methods we will choose appropriate models for the biggest claims. Keywords: parameterization, non-life insurance, claims distribution.
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Interest rates models in continous time
Garajová, Jana ; Cipra, Tomáš (advisor) ; Dostál, Petr (referee)
The core of this work is to introduce the probabilistic techniques used in widely applied financial models and to formulate the term structure of interest rates using the continuous-time no-arbitrage framework. Stochastic processes in this work are mean-reverting, because over the long time horizon, interest rates have the tendency to revert to their average long-term levels. All the short rate models explained are Ito processes based on the Brownian motion, which onebyone define the parameters to best represent the real behavior of interest rates in continuous time. Examples and graphs are provided for illustration of the key results.
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Long-Term Insurance and Permanent Health Insurance
Kočová, Karolína ; Cipra, Tomáš (advisor) ; Šváb, Jan (referee)
This thesis deals with long-term care insurance and disability insurance. Both products are classified as products of private health insurance which is described in the first chapter. We can find characteristics of longterm care and its providers in Czech republic in the second chapter. Further, some numerical methods used in long-term care insurance are stated. The third chapter describes the British model of length of stay in institutional long-term care, the results of the study in the Great Britain are summarized in brief. The fourth chapter deals with characteristics and numerical methods of disability insurance. The fifth chapter displays the use of state model in disability insurance. The emerging costs method is illustrated on simple example. The life tables for disabled people were designed to be used in the calculation. In the conclusion we can find reasoning for the future of products mentioned above on the Czech insurance market.
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Longevity Risk in Life Insurance
Danešová, Zdenka ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
In this thesis we deal with the longevity risk originating from the uncertain future evolution of mortality at adult-old ages. It may emerge in particular because of an unanticipated reduction in mortality rates. That risk is significant for annuity and pension providers. We consider a model portfolio represented by one cohort of recipients of immediate life annuities. We introduce possibilities for assessing the risk of such portfolio. A comparison of the impact of longevity risk is made with random deviations in mortality rates. We also deal with the question of solvency of the insurer by investigating the solvency capital requirement for longevity risk.
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Discrete and limited dependent variables in econometrics
Bejda, Přemysl ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
In the present work we study discrete and limited dependent variables. We begin with binary dependent variables. Then we show an example, where we use the data from psychological area. We work with econometric software EViews and show its possibilities, which are connected with our subject of study. We write procedures for "jackknife" method and simple random sample, compare logit, probit and gompit models and draw a graph of conditional probability of our models. Likewise we work with ordinal dependent variables. We use the same data as in the previous example. It means that we investigate possibilities of EViews and add some procedures for "jackkni ng," simple random sampling and for drawing pictures of conditional probability. Just from theoretical point of view we consider unordered dependent variables. In the next chapter we focus on limited dependent variables. We show theory of censored and truncated explained variables. As an application we show theory of survival analysis, which is used in our last example. Statistical computing is performed in R, because no suitable methods are implemented in EViews.
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Annuity modelling in MTPL
Eštóková, Agáta ; Kočová, Karolína (advisor) ; Cipra, Tomáš (referee)
Title: Annuity modelling in MTPL Author: Bc. Agáta Eštóková Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Karolína Kočová Supervisor's e-mail address: kkocova@koop.cz Abstract: This diploma thesis focuses on the possibilities of using generational mortality tables for third party liability insurance, mainly for bodily injured. It describes the construction of generational mortality tables and the creation of RBNS claims reserves. Besides the demonstration of these models, the work analyzes the results of calculating reserves in accordance with generational mortality tables and actual mortality tables of the Czech Republic. An impor- tant element in provision calculating is the simulation of future life expectancy of the insured, i.e. random generation of life expectancy based on generational mortality data. Characteristics of the distribution of reserves are derived from simulations. Furthermore, we compare the results of stochastic and determi- nistic approach of computing the reserves. Keywords: third party liability insurance, RBNS, annuity, generational morta- lity tables.
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Methods of dynamical analysis of portfolio composition
Meňhartová, Ivana ; Hanzák, Tomáš (advisor) ; Cipra, Tomáš (referee)
Title: Methods of dynamical analysis of portfolio composition Author: Ivana Meňhartová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Tomáš Hanzák, KPMS, MFF UK Abstract: In the presented thesis we study methods used for dynamic analysis of portfolio based on it's revenues. The thesis focuses on Kalman filter and local- ly weighted regression as two basic methods for dynamic analysis. It describes in detail theory for these methods as well as their utilization and it discusses their proper settings. Practical applications of both methods on artificial data and real data from Prague stock-exchange are presented. Using artificial data we demonstrate practical importance of Kalman filter's assumptions. Afterwards we introduce term multicolinearity as a possible complication to real data applicati- ons. At the end of the thesis we compare results and usage of both methods and we introduce possibility of enhancing Kalman filter by projection of estimations or by CUSUM tests (change detection tests). Keywords: Kalman filter, locally weighted regression, multicollinearity, CUSUM test
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