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Analysis of financial time series with economical news headlines
Kalibán, František ; Petrásek, Jakub (advisor) ; Zichová, Jitka (referee)
This thesis is focused on options of improving the estimate of volatility of the given financial time series by analysing the economical news headlines. Because of very large volume of data and correlation between word occurence in headlines, the Principal Component Analysis is used to reduce the dimension of data space. For the elimination of significantly large skewness of dependent variable and the preservation of its normality a Box-Cox transformation is used. Finally, a linear model is constructed and its robustness is analyzed by cross-validation method. The computations were made by R software.
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Econometric Systems of Equations as a Tool for Financial Data Analysis
Vaverová, Jana ; Zichová, Jitka (advisor) ; Krtek, Jiří (referee)
This thesis deals with analysing multivariate financial and economical data. The first section describes various types of econometric systems of equations, vector autoregression and constucting models based on this theory. The second part deals with analysing the dependence of time series of inflation rates on various macroeconomical indicators and reciprocal dependence of two exchange rates time series. All results were obtained by the Mathematica 8.0 software.
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Statistical analysis and modeling of inflation
Baniar, Matúš ; Zichová, Jitka (advisor) ; Hurt, Jan (referee)
Title: Inflation modeling Author: Matúš Baniar Department: Department of probability and mathematical statistics Supervisor: RNDr. Jitka Zichová Dr., Department of probability and mathematical statistics Abstract: Inflation, the growth of the general price level, is a common economic phenomenon, which is a macroeconomic problem. The thesis deals with the me- thods by which it is possible to model inflation and therefore to understand its de- velopment. In the first case, the correlation and regression analysis, which deal with the relationship of two or more variables and the following selection of the appro- priate mathematical model. The model of linear regression is described also with methods by which we analyze its adequacy. Another described method is the analy- sis of one-dimensional time series, which we apply so called Box-Jenkins methodol- ogy. Both approaches are illustrated on real financial data using the software Wol- fram Mathematica 8. Keywords: inflation, correlation analysis, regression analysis, time series
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Statistical techniques for Loss Given Default Modeling
Betíková, Veronika ; Vaníček, Karel (advisor) ; Zichová, Jitka (referee)
Title: Statistical techniques for Loss Given Default Modeling Author: Veronika Betíková Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Karel Vaníček Supervisor's e-mail address: karelvanicek@seznam.cz Abstract: The aim of this thesis is to introduce Loss given default as one of the parameters of credit risk. The thesis discusses the basic characters and meth- ods of LGD calculation. It also points out the common use of linear regression models and generalized linear models which are used in practice to estimate LGD parameter. Individual mathematical models and statistical methods for estima- tions of the parameters of such models are concisely described and consequently applied on simulated data. Keywords: LGD, beta regression, OLS, estimation 1
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Interest Rates
Holotňáková, Dominika ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
This thesis is focused on the study of interest rates, It consists of four chapters. The first chapter provides introduction to this issue, presents basic terminology and different method of interest rate process. The second chapter re- presents theoretical one-factor and two-factor models of interest rates, it is mainly aimed at Vasicek, Dothan and Cox-Ingersoll-Ross model, which are used in the practical part. The third chapter is devoted to internal bank policy, describing the most important factors influencing amount of interest rate and credit limit. The last part of the paper is the practical application of one-factor models on real data. At the beginning of the chapter, we describe methods of parameters esti- mation, which are used for individual models. Numerically estimated parameters are inputs for simulations of yield curves by these models. 1
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Probability distributions in finance
Malec, Jaromír ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
This thesis presents a summary of distributions suitable for modelling returns and losses. First discusses the basic properties of returns and losses, and then on specific distributions. Particular emphasis is placed on the asymmetric distribution and distribution with heavy tails. These distributions are discussed in depth, and the basic properties concerning the behaviour of tails are summarized. It is also supplemented with numerical observations on real data. The motive for writing this work is the inadequacy of symmetric distribution, because they are not good for modelling extreme returns and losses. The work should help people, who are interested in studying asymmetric distribution with heavy tails, as a source of further investigation.
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Selected methods for multivariate financial data analysis
Andráš, Adrián ; Zichová, Jitka (advisor) ; Hurt, Jan (referee)
In practice, we often meet data in the form of observations of several variables at various points in time. These data are called time series. We present various approaches in time series analysis; graphical models, vector autoregres- sive models and vector moving-average models. We try to get information about mutual relationship of the variables and then to model their behavior. The used techniques are illustrated on log returns of monthly average exchange rates. The programs are processed in the software Mathematica 7 and can be found on the CD. 1
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Level Sets of Multivariate Density Functions and their Estimates
Kubetta, Adam ; Hlubinka, Daniel (advisor) ; Zichová, Jitka (referee)
A level set of a function is defined as the region, where the function gets over the specified level. A level set of the probability density function can be considered an alternative to the traditional confidence region because on certain conditions the level set covers the region with minimal volume over all regions with a given confidence level. The benefits of using level sets arise in situations where, for example, the given random variables are multimodal or the given random vectors have strongly correlated components. This thesis describes estimates of the level set by means of a so called plug-in method, which first estimates density from the data set and then specifies the level set from the estimated density. In addition, explicit direct methods are also studied, such as algorithms based on support vectors or dyadic decision trees. Special attention is paid to the nonparametric probability density estimates, which form an essential tool for plug-in estimates. Namely, the second chapter describes histograms, averaged shifted histograms, kernel density estimates and its generalization. A new technique transforming kernel supports is proposed to avoid the so called boundary effect in multidimensional data domains. Ultimately, all methods are implemented in Mathematica and compared on financial data sets.
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Control of Company Risk
Nagy, Gergely ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
In the present thesis we study the most common risks a company faces every day. We deal with risk valuation from different points of view, but mostly the most modern risk measure, the Value at Risk is discussed. We study different ways of VaR esti- mation based on historical data. Further, we study the most common types of risks, market risk, liquidity and credit risk, and operational risks. This work is accompanied with sample examples and a procedure, programmed in the system Mathematica, for illustration and computational purposes.
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Modelování ve finanční analýze
Maďar, Milan ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
In this thesis we study the regional and global linkages as evidence of markets integration of the stock markets in Frankfurt, Amsterdam, Prague the U.S. and the dynamics of volatility transmission of related foreign exchange rates using multivariate GARCH approach. For each of the model classes, a theoretical review, basic properties and estimation procedure are provided. We illustrate approach by applying the models to daily market data. Our two main aims are discussing and report the existence of regional and global stock markets linkages and provide comparison of such multivariate GARCH models on the data sample. We find out that the estimated time-varying conditional correlations indicate limited integration among the markets which implies that investors can benefit from the risk reduction by investigating in the different stock markets especially during the crisis.
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