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Selected topics of multivariate time series analysis in finance
Slívová, Iveta ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
In the present work, we study ARMA model at the beginning, then we write about one-dimensional and multivariate ARCH and GARCH model, further we move on to the multivariate GARCH model. At the end, the principal component decomposition is introduced, it is a procedure to reduce the number of parameters involved in a multivariate GARCH model. The theory is explicated rst on a basic ARMA model, afterwards it is modi ed step by step for the one-dimensional and the multivariate GARCH model. There are solved examples for multivariate ARCH and GARCH model and nancial data are analyzed by means of these models.
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Modelling financial time series
Holubářová, Šárka ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
This diploma thesis deals with modelling nancial time series and especially the changing volatility of nancial returns, which is characteristic for them. The theoretical part of the thesis describes several processes with non-constant conditional variance, which form an alternative to the classical ARMA approach to modelling time series. The focus is mainly on two types of processes - lognormal autoregressive process for conditional variance as an example of process where the conditional variance is independent of past returns, and on ARCH processes which to the contrary are based on dependence of the conditional variance on past returns. The properties of described models are veri ed and demonstrated in a simulation study carried out in Mathematica. Final part of the thesis is dedicated to application of the models to real data and modelling volatility of time series of returns of shares and currency rates. The parameters of the models are estimated and forecasts calculated in Mathematica with partial use of programme XploRe.
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Variable life annuity
Šimlovič, Matej ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
In the first chapter, the thesis contains a description of variable annuity and description of four basic guarantees: guaranteed minimum death benefit, guaranteed minimum accumulation benefit, guaranteed minimum income bene- fit and guaranteed minimum withdrawal benefit. For each of these guarantees, there is a description of principle of the benefit, assumptions of payment, amount of payment and a difference from a product without such guarantee, thus a net benefit from the guarantee. In the second chapter, with additional assumptions, there are deductions of expected values of benefits from the described guaran- tees and numerical calculation of these expected values for both genders, various entering ages and various investment variables. 1
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Holt-Winters method for exponential smoothing
Koritarová, Lenka ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
"his thesis de-ls with the methods of exponenti-l smoothingF et (rst the prin iE ples of exponenti-l smoothing -re expl-inedF e fo us on -si -ppro- hesX sinE gleD dou le smoothing -nd the rolt¡s methodF "hese pro edures -re suit- le for the modeling time series without se-son-l omponentF rowever in pr- ti e there -re frequent time series with se-son-lityF por su h time series the roltE inter¡s method is usedF "his method is -sed just on the prin iples of exponenti-l smooE thingF sn the l-st p-rt of this thesisD there is demonstr-ted using this methods on re-l d-t-F
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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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Annuities under random interest rates
Sviteková, Zuzana ; Cipra, Tomáš (advisor) ; Mazurová, Lucie (referee)
The thesis describes accumulated values of annuities with yearly payments under independent random interest rates. The thesis focuses on general annuities with payments varying in arithmetic and geometric progressions which are important varying annuities. Mean and variance formulae of the final values of the annuities are derived in the thesis. In the beginning (chapter 2) the formulae of the final values of the annuities under xed rates of interest are shown. Chapter 3 is the main part of the thesis. The mean and variance formulae of the final values of the annuities under random rates of interest are proofed here. The thesis is based on the article [4] and [1]. It is especially focused on the article [1] which corrects main outcome of the article [4]. In the end (chapter 4) special cases of the annuites with numerical and graphical solutions are shown.
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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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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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