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Selected problems and methods in multivariate data analysis
Goduľová, Lenka ; Zichová, Jitka (advisor) ; Hurt, Jan (referee)
Title: Selected problems and methods in multivariate data analysis Author: Lenka Goduľová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr. Abstract: The bachelor thesis deals with processing multidimensional data. The task was to apply selected methods on financial data. The thesis is composed of the theoretical section and the analysis of a particular database. The first four chapters deal with basic relations and definitions concerning random vector and variable, multidimensional data and the independence test in a contingency table. The following section is devoted to defining the particular methods selected: cluster analysis and discriminant analysis. In the practical section these methods are applied to a database of clients of a German bank. Keywords: random vector, multivariate distribution, multivariate random variable, contingency table, cluster analysis, discriminant analysis.
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Long range dependence in time series
Till, Alexander ; Prokešová, Michaela (advisor) ; Hurt, Jan (referee)
Title: Long range dependence in time series Author: Alexander Till Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michaela Prokešová, Ph.D. Abstract: The diploma thesis demonstrates the necessity of a study of long range dependence, introduces fractional Gaussian noise and discusses possible definitions of long memory. It is done by notions of ergodic theory and by second moment characteristics and spectral density. These definitions are confronted with the model of fractional Gaussian noise and with intuitive understanding of long range memory. Relations and connections between these criteria are studied as well. The work is restricted to the study of discrete time processes. 1
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Financial risks with copulas
Prelecová, Natália ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The aim of this thesis is the thorough description of the copula theory. It deals with the theory's basic definitions, classes and characteristics. In addition, relations between copulas and dependence measures are explained. Furthermore, we evaluate the possibilities of copula's parametres estimation and selecting the right copula for real data. Then, the copula theory is interconnected with the basic risk measures in finance. We describe the elementary categorization of financial risks and standard risk measurement approaches. We also define basic risk measures with the emphasis on value at risk. Lastly, we present a real data case study of a selected portfolio.
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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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Recursive estimation of models relating discrete-valued variables to continuous-valued ones applied to trading with futures
Svoboda, Miroslav ; Kárný, Miroslav (advisor) ; Hurt, Jan (referee)
This bachelor thesis deals with recursive estimation of a dependence of the models with discrete variables on variables that are either discretely or continuously distributed. To this purpose Bayes formula, described in the first chapter, is used, to which an additional assumption of conditional independence is added so that it can be used dynamically. The second chapter describes an approximation algorithm, which is used for recursive approximation of the density of random variable that has been estimated by the Bayesian equation. The third chapter deals with the application of the whole model on a special form of logistic regression. Results are shown on the examples using simulated data. At last, the model along with approximation algorithm is applied on a trading with futures. Powered by TCPDF (www.tcpdf.org)
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Reliability of systems with redundant subsystems and/or elements
Čáha, Pavel ; Antoch, Jaromír (advisor) ; Hurt, Jan (referee)
The thesis deals with the basic notions of the (system) reliability theory as e.g., failure, time to failure, reliability function, mean time to failure, intensity of failures, etc. It also describes probability distributions that are frequently used in the field of (system) reliability. Fourth chapter is focused on the reliability of basic systems as, e.g., serial, prallel, circle and star, using Boolean algebra and Markov chains. The last part of the thesis describes the simulation of complex systems. This part also includes two programmes. The first one enables a simulation of reliability of basic systems and the second reliability of the network of the building MFF UK, Karlín. Powered by TCPDF (www.tcpdf.org)
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Probability distributions of financial losses
Vacek, Lukáš ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
In this bachelor thesis, selected probability distributions which might appear useful for financial losses modelling are presented. Losses, risk measures and an example with a normality assumption are defined in the first part. Among others, the following distributions are presented in the second part: asymmetric Laplace distribution, skew normal distribution and generalized hyperbolic distribution. We present selected theoretical properties of these distributions. Procedures of a derivation of two asymmetric distributions from their symmetric cases are discribed. The asymmetric Laplace distribution is described more in detail, we also listed the maximum likelihood estimation with its implementation in software Wolfram Mathematica 10. The third part is a short numerical study, where an application of selected distributions is presented on real market data. Test of randomness and goodness of fit tests are performed. Powered by TCPDF (www.tcpdf.org)
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Credit risk
Srbová, Eliška ; Herman, Jiří (advisor) ; Hurt, Jan (referee)
This thesis deals with credit risk and selected methods of its evalua- tion. It is focused on assumptions, calculation methods, results and specifics of the CreditMetrics and the CreditRisk+ models. The CreditRisk+ model analytically determines the portfolio credit losses distribution that is caused by defaults of counterparties. In the CreditMetrics model, the credit migration risk is addition- ally considered and the future portfolio value distribution is calculated using the Monte Carlo simulation. The third approach covered in this thesis is the Solvency II, the set of requirements proposed by the European Union for determination of regulatory capital for insurance companies. In the practical part the three ap- proaches are applied on a set of three portfolios of different credit quality. Their results, particularly the determined level of capital required to cover the risk of unexpected credit losses, are analyzed and compared.
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Contemporary measures of financial risk
Leder, Ondřej ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The main goal of this thesis is to talk about some financial risks and to introduce some methods of measuring them. We place great emphasis on the value at risk, its extension in form of conditional value at risk and introduction of some of its possible alternatives, which are expectile and spectral risk measures. For this it is necessary to introduce some findings of the theory of probability. Our goal is to show the similarity of expectile and quantile, because value at risk is practicaly a quantile. Another goal of this thesis is to show weakness of VaR and to practically illustrate the possibility of using expectile as an alternative to VaR. Powered by TCPDF (www.tcpdf.org)
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Product processes as a tool for financial analysis
Krejčí, Kateřina ; Zichová, Jitka (advisor) ; Hurt, Jan (referee)
This bachelor thesis discusses product processes as a tool for modeling financial time series. The thesis is divided into the theoretical and the practical part. Basic issues are summarized in the theoretical part. Properties of some moments and correlations are described and derived in this part, parameter estimates of a product process are derived subsequently. The practical part deals further with the parameter estimates. The quality of derived parameter estimates is verified in a simulation study in software Mathematica 9 and the proposed estimates are applied to real financial data. Powered by TCPDF (www.tcpdf.org)
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