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Decomposition methods for time series with irregular observations
Hanzák, Tomáš ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
This work deals with extensions of classical exponential smoothing type methods for univariate time series with irregular observations. Extensions of simple exponential smoothing, Holt method, Holt-Winters method and double exponential smoothing which have been developed in past are presented. An alternative method to Wright's modification of simple exponential smoothing for irregular data, based on the corresponding ARIMA process, is suggested. Exponential smoothing of order m for irregular data as a generalization of simple and double exponential smoothing is derived. A similar method using a DLS (discounted least squares) estimation of polynomial trend of order m is derived as well. In all cases the recursive character of these methods is preserved making them easy to implement and high computationally effective. A program in which most of the methods presented here are available is a part of the work. Some numerical examples of their application are also included.
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Median in some statistical methods
Bejda, Přemysl ; Cipra, Tomáš (advisor) ; Hlávka, Zdeněk (referee) ; Víšek, Jan Ámos (referee)
Median in some statistical methods Abstract: This work is focused on utilization of robust properties of median. We propose variety of algorithms with respect to their breakdown point. In addition, other properties are studied such as consistency (strong or weak), equivariance and computational complexity. From practical point of view we are looking for methods balancing good robust properties and computational complexity, be- cause these two properties do not usually correspond to each other. The disser- tation is divided to two parts. In the first part, robust methods similar to the exponential smoothing are suggested. Firstly, the previous results for the exponential smoothing with ab- solute norm are generalized using the regression quantiles. Further, the method based on the classical sign test is introduced, which deals not only with outliers but also detects change points. In the second part we propose new estimators of location. These estimators select a robust set around the geometric median, enlarge it and compute the (iterative) weighted mean from it. In this way we obtain a robust estimator in the sense of the breakdown point which exploits more information from observations than standard estimators. We apply our approach on the concepts of boxplot and bagplot. We work in a general normed vector...
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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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Solvency Internal models
Mertl, Jakub ; Cipra, Tomáš (advisor) ; Mazurová, Lucie (referee) ; Jedlička, Petr (referee)
Title: Solvency Internal models Author: Mgr. Ing. Jakub Mertl Abstract: The subject of thesis is assessment of calculation methods on capital adequacy of currently implemented regulation in insurance industry called Solvency II. The aim of the thesis is to build up a partial internal model fulfilling the condition of Solvency II. The thesis deals with the premium and reserve risks that are essential part of non-life business. Different approaches of risk assessment are described and aggregation of those risks as well. An important part of the thesis is a numerical example illustrating presented methods.
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Econometric systems of simultaneous equations in life insurance
Hendrych, Radek ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
In present work we deal with theoretical and practical issues related to econometric systems of (linear) simultaneous equations. In the first chapter we introduce to theoretical aspects of this problem. We devote considerable space to estimation procedures and comparisons of their properties, mention questions of identification, an inconsistency of OLS-estimates for the simultaneous modeling, tests of hypotheses specific to this area, dynamic systems and constructions of forecasts in models. In the second chapter we introduce selected basic concepts relevant to life insurance. In the third chapter we show the practical application of theoretical knowledge in the event of an econometric model of financial flows in the life insurance company operating on the Czech market. We compare ordinary estimation procedures (2SLS and 3SLS approach), perform some tests, which serve us to verify selected information on the studied model. We show the possibility of using residual bootstrap, including examples of use in the construction of confidence intervals. Finally we analyze several predictions of the estimated model of the life insurance company for predetermined scenarios for the development of selected variables, which is very important from practical point of view.
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Statistical Properties of the Estimate of Non-Life Insurance Technical Reserves
Pechanec, Jan ; Jedlička, Petr (advisor) ; Cipra, Tomáš (referee)
In the presented work we study two different statistical methods for estimating IBNR reserve that is a part of the reserve for outstanding claims reserves. The first method is stochastic version of the Chain ladder method and the second one is a PTF model. We describe theories of the methods and show their different properties. The Chain ladder method does not assume any distribution of claims amount, on the other hand PTF models assume normal distribution of logarithms of incremental data. In practical part of this work we apply both methods on illustrative data and then we compare the results. We inspect especially probabilistic distribution of estimate of reserves and their statistical characteristics. An important part of this work is statistical testing of assumptions of both methods.
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