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Some modifications of models ARCH for financial time series
Nekvinda, Matěj ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This work deals with modelling time series, especially their volatility, by methods based on the ARCH model. In the beginning, we describe the general features of financial time series, afterwards we focus on the ARCH model modifications. The described modifications are GARCH, EGARCH, GJR-GARCH and briefly GARCH-M, IGARCH, FIGARCH and QGARCH. Along with the models, there is a description of their behaviour, which frequently reflects some features of financial time series. We also mention the process of practical financial time series analysis. In the end, we demonstrate the application of GARCH, EGARCH and GJR-GARCH models for modelling values of FTSE 100 index together with diagnostic tests and prediction. 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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Valuatuion of interest rates derivatives through LIBOR market model
Nistorová, Ružena ; Myška, Petr (advisor) ; Zichová, Jitka (referee)
In this thesis, the interest rates derivatives and their valuation based on the future development of interest rates are presented. The Hull-White model focusing on the modeling of the instantaneous spot rates is described in detail. The model is calibrated to the market caplet volatilities and is used to evaluate various interest rates derivatives. The main emphasis is put on the LIBOR market model describing the development of set of forward rates. There are presented and in detail discussed results of the calibration of LMM model on the market swaption volatilities. At the end the two models are compared.
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Nonlinear parametric models for financial time series
Krnáčová, Simona ; Zichová, Jitka (advisor) ; Hudecová, Šárka (referee)
The thesis is dedicated to study of nonlinear parametric models for financial time series. It contains the summary of basic terms of this issues in brief. The next part is dedicated to the survey of different linear and nonlinear models with description of their basic features. Threshold autoregressive model and bilinear model are presented in details. For these two models, basic features, tests for linearity and estimations are introduced. The practical part is based on the theory described in previous chapters. Particular tests for linearity for both models and estimated instruments are analysed on simulated and real data.
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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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Contemporary measures of financial risk
Leder, Ondřej ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The main goal of this work is to talk about some financial risks and to introduce some methods of measuring them. The most important part of this work is 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 needed to give a theoretical framework from the theory of probability. Its goal is to show the similarity of expectile and quantile, because value at risk is practicaly a quantile. Another goal of this fork is to show some weak properties 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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Study of the dependence structure in economic and financial data
Hlavandová, Radana ; Zichová, Jitka (advisor) ; Petrásek, Jakub (referee)
Title: Study of the dependence structure in economic and financial data Author: Radana Hlavandová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr., Department of Probability and Mathematical Statistics Abstract: The thesis focuses on the issue of graphical models as a possible \\method for determining relationships between different variables. The thesis provides a broad theoretical basis for two methods of testing data, the test of zero partial correlation coefficients and the test based on maximum likelihood estimate. The last mentioned approach is a test of a graphical model with a data set on the basis of deviance. The thesis describes the theory of conditional independence and Markov properties as the basis of both tests, which are illustrated by general examples and by an example with real financial data. Keywords: partial correlation coefficients, conditional independence graph, graphical models
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Non-linear models for financial time series and software tools for their analysis
Fučík, Jan ; Zichová, Jitka (advisor) ; Hendrych, Radek (referee)
This thesis deals with some time series models applicable in finance. First, the basic concepts are introduced and the linear AR models are presented. Afterwards, the reader becomes familiar with the nonlinear ARCH volatility models including their properties and the model-building. The generalized GARCH models are briefly mentioned. Another part of the thesis shows the usage of these models to real data in two available software products - R and Mathematica. The programs are compared from the point of the obtained results and the usability for the analysis of financial time series via the explained models. The description of the procedures and the attached CD with the outputs of the programs allow the reader to apply the models on his or her own data.
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Mathematical methods of investment portfolios construction
Kůs, David ; Witzany, Jiří (advisor) ; Zichová, Jitka (referee)
This thesis describes statistical approaches of investment portfolio constructions. The theoretic part presents modern portfolio theory and specific statistical methods used to estimate expected revenue and risk of portfolio. These procedures are specifically selection method, modelling volatility using multivariate GARCH model, primarily DCC GARCH procedure and Bayes approach with Jeffrey's and conjugated density. The practical part of the thesis covers application of above mentioned statistical methods of investment portfolio constructions. The maximization of Sharp's ratio was chosen as optimization task. Researched portfolios are created from Austria Traded Index issues of shares where suitable time series of historical daily closed prices. Results attained within assembled portfolios in two year investment interval are later compared.
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