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Determination of thickness refinement using STEM detector segments
Skoupý, Radim ; Krzyžánek, Vladislav
Quantitative STEM imaging together with Monte Carlo simulations of electron scattering in solids can bring interesting results about properties of many thin samples. It is possible to determine thickness of a sample, to calculate mass of particles and measure mass per length/area. Appropriate calibration is one of the crucial parts of the method. Even a small error or inaccuracy in detector response to electron beam either blanked or full brings significant error into thickness determination. This problem can be overcome by parallel STEM imaging in more segments of the detector. Comparing more segments gives a possibility to use a signal from different segments for different thicknesses of a sample. Accuracy of individual parts of the detector depends on the captured signal quantity. It is desirable to use such a STEM detector segment that provides the greatest signal change to a unit of thickness. To demonstrate the usage, we used a sample of Latex nanospheres placed on thin carbon lacey film, diameter of the nanospheres was around 600 nm in order to compare the results from different detector segments. Thanks to the known thickness of the sample (calculated from its geometrical shape), it is possible to estimate the optimal acquisition settings and post processing steps with the known and the true state of the sample.
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The Evaluation of the Investment Project
Koštur, Petr ; Poláček, Tomáš (referee) ; Luňáček, Jiří (advisor)
This master’s thesis deals with a comprehensive evaluation of the company's investment related to the purchase of construction machinery. All calculations are performed according to the theoretical basis introduced in the beginning. To evaluate the effectiveness of the investment, static and dynamic methods are used, together with the sensitivity analysis of individual risk factors. The probability of possible scenarios is determined using a Monte Carlo simulation. To conclude, recommendations whether the project should be implemented is given.
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Econometric methods of change detection
Dvoranová, Romana ; Prášková, Zuzana (advisor) ; Hušková, Marie (referee)
Detection of structural changes in time series is a topic with increasing pop- ularity among econometricians over the last decades. The main aim of this thesis was to review and compare the classical and modern econometric meth- ods of structural change detection and unit root testing. A recent method for testing a one-time break in at most linear trend function of a series without prior knowledge about the stationary or unit root nature of the error compo- nent proposed by Perron and Yabu (2009b) was studied. Subsequently, it was combined with the unit root test that allows for a break in trend proposed by Kim and Perron (2009) to examine the nature of the error component. All the methods for change detection and unit root testing were compared in a Monte Carlo simulation study that indicated significant improvement in power of the Perron-Yabu and Kim-Perron tests against most alternatives compared to the classical methods. However, all tests demonstrated poor performance in case of a quadratic trend function. Finally, the tests were employed in a practical ex- ample to examine the properties of the quarterly GDP time series of the Czech Republic. 1
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Pricing Options Using Monte Carlo Simulation
Dutton, Ryan ; Dědek, Oldřich (advisor) ; Červinka, Michal (referee)
Monte Carlo simulation is a valuable tool in computational finance. It is widely used to evaluate portfolio management rules, to price derivatives, to simulate hedging strategies, and to estimate Value at Risk. The purpose of this thesis is to develop the mathematical foundation and an algorithmic structure to carry out Monte Carlo simulation to price a European call option, investigate Black-Scholes model to look into the parallel between Monte Carlo simulation and Black-Scholes model, provide a solution for Black-Scholes model using Lognormal distribution of a stock price rather than solving Black-Scholes original partial differential equation, and finally compare the results of Monte Carlo simulation with Black- Scholes closed-form formula. Author's contribution can be best described as developing the mathematical foundation and the algorithm for Monte Carlo simulation, comparing the simulation results with the Black-Scholes model, and investigating how path-dependent options can be implemented using simulation when closed-form formulas may not be available. JEL Classification C02, C6, G12, G17 Keywords Monte Carlo simulation, Option pricing, Black-Scholes model Author's e-mail ryandutton4@gmail.com Supervisor's e-mail oldrich.dedek@fsv.cuni.cz
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Actuarial and Exposure-based Models for Hail Peril
Drobuliak, Matúš ; Pešta, Michal (advisor) ; Hlubinka, Daniel (referee)
Title: Actuarial and Exposure-based Models for Hail Peril Author: Bc. Matúš Drobuliak Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta, Ph.D., Department of Probability and Mathe- matical Statistics Abstract: This thesis covers an introduction to catastrophe modelling and focuses on statistical methods for extreme events. This includes methods of estimating parameters of claim distribution with a focus on probability weighted moments estimation technique. Furthermore, times series modelling, skew t-distribution, and two model clustering techniques are examined as well. This is later utilised in the practical application part of this thesis, which uses real data provided by an insurance company operating in the Czech Republic. Probability distribution fitting of large claims caused by hailstorms and Monte Carlo simulation of future losses are demonstrated later. Keywords: Catastrophe modelling, Hail peril, Probability weighted moments, Extreme events, ARMA-GARCH, Monte Carlo simulation iii
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Capital market efficiency in the Ising model environment: Local and global effects
Krištoufek, Ladislav ; Vošvrda, Miloslav
Financial Ising model is one of the simplest agent-based models (building on a parallel between capital markets and the Ising model of ferromag- netism) mimicking the most important stylized facts of financial returns such as no serial correlation, fat tails, volatility clustering and volatility persistence on the verge of non-stationarity. We present results of Monte Carlo simulation study investigating the relationship between parameters of the model (related to herding and minority game behaviors) and crucial characteristics of capital market e ciency (with respect to the e cient market hypothesis). We find a strongly non-linear relationship between these which opens possibilities for further research. Specifically, the existence of both herding and minority game behavior of market participants are necessary for attaining the e cient market in the sense of the e cient market hypothesis.
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Cost planning of PPP projects in the Czech Republic
Ehrenberger, Marek ; Teplý, Petr (advisor) ; Chytilová, Julie (referee)
English The thesis explores the topic of cost planning of Public-Private-Partnership (PPP) projects in the Czech Republic, especially with respect to institutional settings and road infrastructure. First, the PPP concept is introduced from a theoretical perspective and compared to traditional public procurement. Then the financing of PPP projects is discussed in the context of project finance and the European PPP market. The main part of the thesis focuses on public procurement of road infrastructure and the advantages of the PPP organizational structure. Initially, flaws of the procurement institutions are identified and a number of solutions suggested. The solutions cover four main areas: improvement of procurement laws, better qualifications of public officials, strategic planning of needed roads and asset management perspective on the existing infrastructure. The question whether Czech institutions are hindering the potential of PPP projects is answered positively. Follows a thorough empirical analysis of a World Bank PPP model for highways through a Monte Carlo simulation. A particular case of R35 motorway is evaluated as a PPP project and key drivers of public and private NPV are identified and compared across three different scenarios. Heavyweight traffic intensity, its toll revenue and...
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Cost planning of PPP projects in the Czech Republic
Ehrenberger, Marek ; Teplý, Petr (advisor) ; Chytilová, Julie (referee)
English The thesis explores the topic of cost planning of Public-Private-Partnership (PPP) projects in the Czech Republic, especially with respect to institutional settings and road infrastructure. First, the PPP concept is introduced from a theoretical perspective and compared to traditional public procurement. Then the financing of PPP projects is discussed in the context of project finance and the European PPP market. The main part of the thesis focuses on public procurement of road infrastructure and the advantages of the PPP organizational structure. Initially, flaws of the procurement institutions are identified and a number of solutions suggested. The solutions cover four main areas: improvement of procurement laws, better qualifications of public officials, strategic planning of needed roads and asset management perspective on the existing infrastructure. The question whether Czech institutions are hindering the potential of PPP projects is answered positively. Follows a thorough empirical analysis of a World Bank PPP model for highways through a Monte Carlo simulation. A particular case of R35 motorway is evaluated as a PPP project and key drivers of public and private NPV are identified and compared across three different scenarios. Heavyweight traffic intensity, its toll revenue and...
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Fractal Dimension and Efficient Markets
Máková, Barbora ; Krištoufek, Ladislav (advisor) ; Víšek, Jan Ámos (referee)
The efficient market hypothesis is one of the most important propositions in finance theory and has been subjected to years of rigorous empirical testing. We examine power of a new tool for evaluating market efficiency, fractal dimension. Characteristics and abilities of fractal dimension measure are explored through extensive Monte Carlo simulations. We prove that it provides an accurate evaluation of market's efficiency and its changes. This approach is highly innovative and creates new possibilities for examination of markets. The uniqueness of fractal dimension is in its ability to assign a numerical ranking to examined series describing the level of (in)efficiency; it is accurate for small samples of observations and quickly reflects changes in market efficiency structure. Powered by TCPDF (www.tcpdf.org)
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Sequential Monte Carlo Methods
Sobková, Eva ; Zikmundová, Markéta (advisor) ; Prokešová, Michaela (referee)
Monte Carlo methods are used for stochastic systems simulations. Sequential Monte Carlo methods take advantage of the fact that observations are coming sequentially. This allows us to refine our estimate sequentially in time We introduce a State Space Model as a Hidden Markov Model. We describe Perfect Monte Carlo Sampling, Importance Sampling, Sequential Importance Sampling and discuss advantages and disadvantages of these methods. This discussion brings us to add a resampling step in Sequential Importance Sampling and introduce Particle Filter and Particle Marginal Metropolis-Hastings algorithm. We choose a Hidden Markov Model used for stochastic volatility modeling and make a simulation study in Wolfram Mathematica, version 8.
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