
Backtesting ValueatRisk: Comparison of selected approaches
Šedivý, Milan ; Hendrych, Radek (advisor) ; Hurt, Jan (referee)
This thesis focuses on the evaluation of different backtesting methods that are routinely applied to one of the most commonly used risk measure Value atRisk. The main goal of this thesis is to present approaches used to backtest ValueatRisk (including an introduction to common methods associated with ValueatRisk forecasting). These statistical evaluation methods are then applied to historical data from the years 2005 to 2010, during which we experienced two major financial crises. Afterwards, the output of our analysis is thoroughly discussed. 1

 

Linear and nonlinear autoregressive models for time series from economics and finance
Cvetković, Jelena ; Zichová, Jitka (advisor) ; Hendrych, Radek (referee)
This bachelor thesis deals with linear and nonlinear autoregressive models for time series from economics and finance. It consists of theoretical and practical part. In theoretical part, the reader acquaints with terms connected to random proces ses; then autoregressive and threshold autoregressive time series are introduced, their general properties are derived, possible ways of forecasting are described and ways of parameters estimation are presented. Furthermore, test for threshold autoregression is introduced. The practical part is divided into simulation study, where the quality of estimations and the power of the test is examined on simu lated time series, and into application on real data, where the acquired findings are utilized on time series of share prices of the company ČEZ. 1


Econometric Modelling and Forecasting of Natural Gas Spot Prices
Kubišová, Barbora ; Hendrych, Radek (advisor) ; Hudecová, Šárka (referee)
The thesis deals with modeling and forecasting of natural gas spot prices, con sumption of natural gas and average daily temperature. We assume that these three variables are influenced by each other, because as temperature decreases, consumption increases, which in turn increases the price with the increasing de mand. Therefore, we propose to model these variables by vector autoregression. We compare this model with onedimensional models where for each one we build a model from the ARMAGARCH class. Models are estimated using historic va lues and then designed models are used to simulate scenarios. Analysis of scenarios provides information to gas supply companies estimates of portfolio consumption and financial flows related to the purchase concerning natural gas. 1


Econometric models of national economies
Hála, Petr ; Hendrych, Radek (advisor) ; Hurt, Jan (referee)
The present thesis deals with multiple econometric equations systems which might provide a useful insight into the national economy modelling. It takes into account possible pitfalls of common practices. It introduces the theory and estimation methods of multiple econometric equations systems. It also discusses the equality of savings and investment and the theory of money. Furthermore, it briefly analyses Klein's model I from a theoretical point of view and uses the threestep least squares method in order to estimate it. Partial modifications of this model are suggested and implemented. The quality of the competitive models is evaluated employing the predictive criterion. Consequently, the canonical NK DSGE model is derived and subjected to theoretical criticism. The thesis debates doubts on the relevance of the NK IS curve and argues that Lucas's critique is still valid. A generalized method of moments is used to implement the NK DSGE model. Finally, this model is briefly compared with Klein's model I.


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


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 zeroinflated 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.


ValueatRisk 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 wellknown 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


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 selfweighted recursive estimation algorithms for several classic univariate conditional heteroscedasticity models, namely for the ARCH, GARCH, RiskMetrics EWMA, and GJRGARCH 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 timevarying orthogonal transformation, which enables to employ the constant conditional correlation scheme. The correspond ing model is implemented by using a nonlinear discretetime state space representation. The proposed approach is compared with other commonly applied models. It demon strates its...


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 outofthe money options, the other focusing on producing a smooth state price density and a wellfitting IV smile. Powered by TCPDF (www.tcpdf.org)
