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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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Nonlinear nonparametric models for financial time series
Klačanská, Júlia ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The thesis studies nonlinear nonparametric models used in time series analy- sis. It gives basic introduction to the time series and states different nonlinear nonparametric models including their estimates. Special attention is paid to three of them, CHARN, FAR and AFAR model. Their properties and esti- mation techniques are presented. We also show techniques that select values of the parametres used further in estimation methods. The properties of time series models are investigated in simulation and real data studies. 1
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Software products for financial time series analysis
Vlasáková, Romana ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The present work deals with selected methods suitable to work with financial time series. Firstly, univariate linear models ARMA are introduced, followed by the description of volatility models ARCH and their generalization to GARCH models. There are many modifications of standard GARCH models designed with respect to the nature of financial data, some of which are presented. Another part of the work dealing with multiple time series focuses on VAR models and bivariate GARCH models. The most important part of the work are practical examples of building the theoretically described models in various types of software with built-in procedures for time series analysis. We apply five different types of commercial and non-commercial software, namely EViews, Mathematica, R, S-PLUS and XploRe. The used software products are presented and compared in terms of their capabilities and the results obtained for particular methods.
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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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Seasonality and periodicity in time series
Musil, Karel ; Jonáš, Petr (advisor) ; Cipra, Tomáš (referee)
This work deals with periodicity and seasonality in time series. After a time series periodicity topic is introduced, a seasonal component of time series and a seasonal adjustment is presented. Then basic approaches, used in current practice, are introduced. These are classic model approach, Box-Jenkins methodology, and spectral analysis. The described seasonal adjustment techniques are applied to the time series of the Czech import, export, and foreign trade balance. A brief description of potential problems, which are connected to the seasonal adjustment and are common in practice, is a part of the example as well.
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Retirement planning
Langová, Nadežda ; Cipra, Tomáš (advisor) ; Hurt, Jan (referee)
The thesis is concerned with optimal retirement pension planning in the framework of the Czech pension system. The work proposes an unavoidable reform in order to compensate for adverse demographic trends. Subsequently, it introduces mathematical methods for future old-age pension determination in private pensions. Equally, the thesis deals with optimal pension strategies: when the benefits of individual old-age insurance outgrow those of institutionalised pension insurance and vice versa. A particular aspect of the reform where participants can partially opt out from the compulsory pillar and become part of the new system is discussed with emphasis on the opt-out accompanying factors.
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Option Pricing
Moravec, Radek ; Hurt, Jan (advisor) ; Cipra, Tomáš (referee)
Title: Option Pricing Author: Radek Moravec Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Jan Hurt, CSc., Department of Probability and Mathematical Statistics In the present thesis we deal with European call option pricing using lattice approaches. We introduce a discrete market model and show a way how to find an arbitrage price of financial instruments on complete markets. It's equal to the discounted value of future expected cash flow. We present the binomial option pricing model and generalize it into multinomial model. We test the resulting formula on real market data obtained from NYSE and NASDAQ. We suggest a parameter estimate method which is based on time series of historical observations of daily close price. We compare calculated option prices with their real market value and try to explain the reasons of the differences. 1
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Multidimensional risk measures
Chromíková, Dana ; Kopa, Miloš (advisor) ; Cipra, Tomáš (referee)
This thesis deals with multiperiod risk measures and multiperiod models with these risk measures in the objective are formulated. Multiperiod models consider the possibility of an intermediate actions within the investment horizont and represent the real situation in a better way than one-period models. First the basic properties for one-period risk measures are summarized. Then multiperiod risk measures are de ned and several ways of construction concrete risk measures are discussed as extension of one-period risk measures. Multiperiod portfolio selection mean-risk models with di erent risk measures are formulated, transaction costs are included and short sales are not allowed. Using scenario approach the analysis on real data is performed and optimal strategies for one-period and multiperiod models are compared. A transaction costs e ect on optimal strategy is examined.
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