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Multivariate goodness-of-fit tests
Kuc, Petr ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
In this thesis we introduce, implement and compare several multivariate goodness-of-fit tests. First of all, we will focus on universal mul- tivariate tests that do not place any assumptions on parametric families of null distributions. Thereafter, we will be concerned with testing of multi- variate normality and, by using Monte Carlo simulations, we will compare power of five different tests of bivariate normality against several alternati- ves. Then we describe multivariate skew-normal distribution and propose a new test of multivariate skew-normality based on empirical moment genera- ting functions. In the final analysis, we compare its power with other tests of multivariate skew-normality. 1
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Application of Monte Carlo simulations in banking
Boruta, Matěj ; Teplý, Petr (advisor) ; Fučík, Vojtěch (referee)
Currently, banking is exposed to huge market risks. One of those risks is occurrence of negative interest rates in the EU. Nowadays, it is important to use sophisticated and modern measurement tools and approaches to measure and manage banking risks. One of those methods is Monte Carlo simulation. This bachelor thesis is aimed at analysis and prediction of 3-month maturity Prague Interest Offer Rate (PRIBOR) for 3, 6 and 12 months with using Monte Carlo simulations. It was found that this method is suitable for prediction market variables with low volatility. If anybody uses this method, it is necessity to have in mind all pitfalls and assumptions, that this method includes, as an adequate random generated number of scenarios, approximation of correct probability distribution, independence of dataset and not least, as far as possible, to focus on factors generating randomness of market variable and not the prices, that express rather consequences of randomness than its cause. Further, the Monte Carlo prediction was compared with prognosis of the Czech Nation Bank and it was found that Monte Carlo prediction is more accurate for short term predictions. 12-month prediction of Monte Carlo simulation discovered also possible occurrence of negative interest rate at 0,05% level of probability in compare to the Czech National Bank prognosis, where was no negative interest rate predicted.
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Monte Carlo simulations of electron scattering in scanning transmission electron microscopy
Záchej, Samuel ; Hrubanová, Kamila (referee) ; Krzyžánek, Vladislav (advisor)
This thesis deals with an electron scattering in STEM microscopy on objects with dif-ferent shapes, such as cuboid, sphere and hollow capsule. Monte Carlo simulations are used for description of multiple electron scattering. Except the theoretical analysis of the electron scattering and simulation methods, the thesis contains design and realiza-tion of an algorithm simulating electron scattering in given objects. In addition, there is a design for robustness evaluation of the simulation, based on comparison between results and known signals for a given object. Reliability of the algorithm was verified by experimental measurements of the electron scattering on a carbon layer.
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A comparison of effective and functional connectivity methods in fMRI
Gajdoš, Martin ; Schwarz, Daniel (referee) ; Jan, Jiří (advisor)
Functional magnetic resonance imaging (fMRI) is recent important method, used in neuroimaging. The aim of this thesis is to develop software tool for comparison of two methods for functional and effective connectivity estimation. In this thesis are described the basics of magnetic resonance imaging, fMRI, basic terms of fMRI experiments and generally are described methods of functional and effective connectivity. Then are more detailed mentioned methods of dynamic causal modeling (DCM), Granger causal modeling (GCM) and independent component analysis (ICA). Practical implementation of DCM in toolbox SMP and ICA in toolbox GIFT is also mentioned. In purpose to describe behavior of DCM and GCM in dependence on several parameters are performed Monte Carlo simulations. Then the concept and realization of software tool for simulating connectivity and comparison of DCM and GCM are described. Finally results of DCM and GCM comparison and results of Monte Carlo simulations are discussed.
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Valuation of the company Únětický pivovar a.s.
Podolský, Jiří ; Brabenec, Tomáš (advisor) ; Hamplová, Barbora (referee)
The thesis aims to determine the value of equity of the company Únětický pivovar, a. s. as of January 1st, 2014. It does not have a theoretical and practical part as usual. It is a complex unit, in which the concepts and methods are explained straight away. The paper is divided into five main parts. Introduction of company profile is followed by strategic analysis, which deals with analysis of the external potential of beer market and internal potential of the company. The next part, financial analysis, gives a picture of financial results, health and stability of the company and other comparable breweries. The output of the chapter Value drivers is the financial plan, which is crucial for company valuation using the method of discounted cash flow (DCF). The final chapter contains an application of Monte Carlo simulations, which enriches the conclusions by offering probability distribution of the value of the company.
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Modeling of nucleolar self-assembly
Blažíková, Michaela ; Heřman, P. ; Malínský, Jan
Mammalian cell nucleoli disassemble at the beginning of mitosis and reassemble again during telophase and the early G1. Dynamics of this process was studied using a model based on entropy driven self-assembly of pre-ribosomal particles generated in a single biosynthetic source. Monte Carlo simulations revealed that such model can explain formation of a large aggregate, a nucleolus, in the vicinity of the source. We examined influence of nucleoplasm properties on dynamics of the aggregate formation.
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Nedávné pokroky v molekulárních simulacích termodynamického chování tekutých soustav.
Aim, Karel ; Lísal, Martin ; Nezbeda, Ivo ; Ungerer, P. ; Teuler, J.-M. ; Rousseau, B.
An overview of the recent developments in molecular computer simulation techniques used to calculate phase equilibria and thermodynamic properties of fluid systems is given. Particular attention is paid to the methodologies as follows: (i) reaction Gibbs ensemble Monte Carlo (RGEMC), which allows accurate phase equilibrium predictions for mixtures by employing experimental pure-component vapour pressure data in the computational procedure (ii) direct Monte Carlo simulation of Joule-Thomson processes, (iii) Monte Carlo simulations at fixed entropy, and (iv) an implemented parallelized sampling version of the Gibbs ensemble Monte Carlo (GEMC), which by-passes the physical transfer of complex molecules between boxes representing different phases by computing the chemical potential in an NVT ensemble (and is applicable also to flexible molecules). Example applications of the considered techniques for real fluid systems ar
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Derivative Pricing Using Monte Carlo Simulations
Burešová, Jana ; Witzany, Jiří (advisor) ; Málek, Jiří (referee)
Pricing of more complex derivatives is very often based on Monte Carlo simulations. Estimates given by these simulations are derived from thousands of scenarions for the underlying asset price developement. These estimates can be more precise in case of higher number of scenarions or in case of modifications of a simulation mentioned in this master thesis. First part of the thesis includes theoretic description of variance reduction techniques, second part consists of implementation of all techniques in pricing a barrier option and of their comparison. We conclude the thesis by two statements. The former one says that usage of each technique is subject to simulation specifics, the latter one recommends to use MC simulations even in the case a closed-form formula was derived.
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