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Stochastic models in theory of the firm
Vaněk, Petr ; Kopa, Miloš (advisor) ; Hendrych, Radek (referee)
The goal of this bachelor's thesis is the stochastic extension of deterministic models belonging to the theory of the firm. The thesis deals specifically with finding optimal solutions for deterministic and stochastic problems of production maximization, cost minimization and profit maximization. At first, basic concepts of theory of the firm are introduced in this work and also there are listed deter- ministic optimization problems with their solutions. Then these deterministic models are extended by random input prices and random demand. A stochastic programming solution is proposed for each extension. The end of this bachelor's thesis deals with the practical stochastic problem of production maximization, which illustrates the dependence of the optimal solution on the input parameters of the model. 1
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Mixed Poisson models for claim counts
Hauptfleisch, Filip ; Pešta, Michal (advisor) ; Hendrych, Radek (referee)
The thesis summarizes the theory of mixed Poisson models. Poisson distri- bution is one of the popular distributions in modelling count data, but its use is limited because it requires equidispersion. Because of this we introduce both con- tinuous and finite mixtures. From continuous mixtures the main representative is the negative binomial model, which arises as Poisson Gamma mixture, while from discrete models we deal mainly with zero-inflated models and hurdle models. For these models we use the maximum likelihood estimates of their parameters. In the end we apply these models to fit automobile insurance data from Australia, where we use MLE to fit Poisson regression, negative binomial regression and Poisson hurdle regression.
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Value-at-Risk Calculation Using Extreme Value Theory
Lipták, Patrik ; Hendrych, Radek (advisor) ; Mazurová, Lucie (referee)
This diploma thesis studies extreme value theory and its application in finan- cial risk management, when focusing on computation of well-known risk measure - Value at Risk (VaR). The first part of the thesis reviews theoretical background. In particular, it rigorously discusses the extreme value theory when emphasi- zing fundamentals theorems and their consequences followed by the summary of methods based on this theory, specifically, Block Maxima method, Hill met- hod and Peaks over Threshold method. Moreover, specific issues that may arise in such applications and ways how to deal with these problems are described. The second part of the thesis contains extensive empirical study, which together with theoretical foundings applies each of the examined method to real market data of the closing prices of Dow Jones Industrial Average stock index, stocks of JPMorgan and stock index Russell 2000 in order to compare methods based on extreme value theory together with the classic methodology RiskMetrics. 1
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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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Implied volatility modelling of options
Jahn, Daniel ; Kopa, Miloš (advisor) ; Hendrych, Radek (referee)
This text presents an analysis of constrained local polynomial estimation used to extract the implied volatility smile from options data. The optimization constraint derived from the state price density ensures the no arbitrage condition. The analysis contains an evaluation of the role of different parameters, such as the degree of the polynomial, kernel type and bandwidth, on the resulting IV smile. Two main approaches are suggested, one attempting to reflect the problematic case of the out-of-the- money options, the other focusing on producing a smooth state price density and a well-fitting IV smile. Powered by TCPDF (www.tcpdf.org)
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Unit root testing with applications to financial time series
Pechmanová, Kateřina ; Zichová, Jitka (advisor) ; Hendrych, Radek (referee)
This work deals with linear ARMA processes, which are intended to describe the behavior of time series, and also with analysis of selected time series. First, the basic concepts are introduced together with the descriptions of the ARMA models. Further, the Dickey-Fuller test for a unit root, as an approach to the verification of nonstationary time series, is introduced. An important part is the practical application of these models and tests on simulated and real data. Real analyzed data capture developments in the exchange rate of Czech crown against Euro. All calculations were performed in the Mathematica software. Powered by TCPDF (www.tcpdf.org)
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Quantitative Methods of Risk Control
Marcinek, Daniel ; Hurt, Jan (advisor) ; Hendrych, Radek (referee)
This thesis deals with stock modelling using ARCH and GARCH time series. Important aspect of stock modelling is to capture volatility correctly. Volatility in finance is usually defined as a standard deviation of asset returns. Many different models, which are summarized in the first part of this thesis, are used to model volatility. This thesis focus on multivariate volatility models including multivariate GARCH models. An approach to constructing a conditional maximum likelihood estimate to these methods is given. Discussed theory is applied on real financial data. In numeric application there is a construction of a volatility estimates for two specific stocks using models described in the first part of this thesis. Using the same financial data various bivariate models are compared. Based on comparison using maximum likelihood a specific model for these stocks is recommended. Powered by TCPDF (www.tcpdf.org)
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Determinants forming attitudes of selected political parties from EU27 countries to the Turkish enlargement of the EU
Hendrych, Radek ; Šlosarčík, Ivo (advisor) ; Kostelka, Filip (referee)
The present thesis analyzes possible determinants shaping attitudes of selected relevant political parties from the EU27 Member States to the potential Turkish accession to the European Union. Bilateral relationships between the EU and the Turkish Republic have been evolving multifariously and long-windedly. However, the question of the direct Turkish participation in the EU's project remains unresolved, and still resonates across all stakeholders. The phenomenon of the eventual Turkish joining is a very topical issue. In particular, the views of the political parties on this particular problem are studied, since these subjects operate with an exclusive position in representative democracies. They symbolize the necessary interconnection between the state and society. Moreover, in the context of the eventual EU enlargement to Turkey, they will likely discuss its confirmation in parliamentary procedures, or they will mobilize voters and form their attitudes in the case of ratification referenda. The present thesis distinguishes between two main groups of explanatory variables. In regarding to the accepted theoretical framework, these are supposed to explicate the views of the selected political parties on the eventual Turkish enlargement qualifiedly. Particularly, the ideological and (general)...
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Estimation of parameters of clipped time series
Flimmel, Samuel ; Hudecová, Šárka (advisor) ; Hendrych, Radek (referee)
In some situations we cannot observe the original time series and instead, we record only binary data which express whether the values of the original series exceeded a certain threshold or not. The thesis deals with estimation of characteristics of the original series constructed from the binary (so called clipped or hard-limited) data, in particular in Gaussian ARMA models. We summarize some basic characteristics of the clipped series and describe their relation to the original ones. Some practical examples are provided as well. The estimation of parameters in AR(p) model is shown for the case of zero threshold. Using a similar approach, an estimator of the MA(1) model parameter is proposed and its properties are studied with emphasis on asymptotic variance. Subsequently, we propose an estimation procedure for AR(p) and MA(1) models with unknown (non-zero) threshold. The behaviour of our estimators is investigated in a simulation study, which provides a comparison with estimators constructed from the original data. Finally, a real data analysis is presented for an illustration. Powered by TCPDF (www.tcpdf.org)
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Econometric systems of simultaneous equations in life insurance
Hendrych, Radek
Title: Econometric systems of simultaneous equations in life insurance Author: Radek Hendrych Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Tomáš Cipra, DrSc. Supervisor's e-mail address: cipra@karlin.mff.cuni.cz Abstract: 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....
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