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Advanced methods of interest rate models calibration
Holotňáková, Dominika ; Witzany, Jiří (advisor) ; Branda, Martin (referee)
This thesis is focused on the study of advanced methods of interest rate mo- dels calibration. The theoretical part provides introduction to basic terminology of financial mathematics, financial, concretely interest rate derivatives. It presents interest rate models, it is mainly aimed at HJM approach and describes in detail the Libor market model, then introduces the use of Bayesian principle in calcula- ting the probability of MCMC methods. At the end of this section the methods of calibration of volatility to market data are described. The last chapter consists of the practical application of different methods of calibration Libor market model and consequently pricing od interest rate swaption. The introduction describes procedure of arrangement of input data and process of pricing of interest rate derivatives. It is consequently used for the valuation of derivative contract accor- ding to mentioned methods. 1
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Influence of velocity model uncertainty in earthquake source inversions
Halló, Miroslav ; Gallovič, František (advisor) ; Duputel, Zacharie (referee) ; Vavryčuk, Václav (referee)
Title: Influence of velocity model uncertainty in earthquake source inversions Author: Miroslav Halló Department: Department of Geophysics Supervisor: doc. RNDr. František Gallovič, Ph.D., Department of Geophysics Abstract: Earthquake ground motions originate from rupture processes on faults in Earth. Constraints on earthquake source models are important for better un- derstanding of earthquake physics and for assessment of seismic hazard. The source models are inferred from observed waveforms by inverse modeling, which is subject to uncertainty. For large tectonic earthquakes the major source of un- certainty is an imprecise knowledge of crustal velocity model. The research topic of this Thesis is the influence of the velocity model uncertainty on the inferred source models. We perform Monte-Carlo simulations of Green's functions (GFs) in randomly perturbed velocity models to reveal the effects of the imprecise veloc- ity model on the synthetic waveforms. Based on the knowledge gained, we derive closed-form formulas for approximate covariance functions to obtain fast and effective characterization of the GFs' uncertainty. We demonstrate that approxi- mate covariances capture correctly the GF variability as obtained by the Monte- Carlo simulations. The proposed approximate covariance functions are...
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Development of trainable policies for spoken dialogue systems
Le, Thanh Cong ; Jurčíček, Filip (advisor) ; Peterek, Nino (referee)
Abstract Development of trainable policies for spoken dialogue systems Thanh Le In humanhuman interaction, speech is the most natural and effective manner of communication. Spoken Dialogue Systems (SDS) have been trying to bring that high level interaction to computer systems, so with SDS, you could talk to machines rather than learn to use mouse and keyboard for performing a task. However, as inaccuracy in speech recognition and inherent ambiguity in spoken language, the dialogue state (user's desire) can never be known with certainty, and therefore, building such a SDS is not trivial. Statistical approaches have been proposed to deal with these uncertainties by maintaining a probability distribution over every possible dialogue state. Based on these distributions, the system learns how to interact with users, somehow to achieve the final goal in the most effective manner. In Reinforcement Learning (RL), the learning process is understood as optimizing a policy of choosing action conditioned on the current belief state. Since the space of dialogue...
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Approximative Bayes methods for belief monitoring in spoken dialogue systems
Marek, David ; Jurčíček, Filip (advisor) ; Žabokrtský, Zdeněk (referee)
The most important component of virtually any dialog system is a dialogue manager. The aim of the dialog manager is to propose an action (a continuation of the dialogue) given the last dialog state. The dialog state summarises all the past user input and the system input and ideally it includes all information necessary for natural progress in the dialog. For the dialog manager to work efficiently, it is important to model the probability distribution over all dialog states as precisely as possible. It is possible that the set of dialog states will be very large, so approximative methods usually must be used. In this thesis we will discuss an implementation of approximate Bayes methods for belief state monitoring. The result is a library for dialog state monitoring in real dialog systems. 1
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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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Advanced methods of interest rate models calibration
Holotňáková, Dominika ; Witzany, Jiří (advisor) ; Branda, Martin (referee)
This thesis is focused on the study of advanced methods of interest rate mo- dels calibration. The theoretical part provides introduction to basic terminology of financial mathematics, financial, concretely interest rate derivatives. It presents interest rate models, it is mainly aimed at HJM approach and describes in detail the Libor market model, then introduces the use of Bayesian principle in calcula- ting the probability of MCMC methods. At the end of this section the methods of calibration of volatility to market data are described. The last chapter consists of the practical application of different methods of calibration Libor market model and consequently pricing od interest rate swaption. The introduction describes procedure of arrangement of input data and process of pricing of interest rate derivatives. It is consequently used for the valuation of derivative contract accor- ding to mentioned methods. 1
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Evolution of brain size in bats (Chiroptera)
Králová, Zuzana ; Němec, Pavel (advisor) ; Kratochvíl, Lukáš (referee)
According to the prevailing doctrine, brain size has mainly increased throughout the evolution of mammals and reductions in brain size were rare. On the other hand, energetic costs of developing and maintaining big brain are high, so brain size reduction should occur every time when the respective selective pressure is present. Modern phylogenetic methods make it possible to test the presence of evolutionary trend and to infer the ancestral values of the trait in question based on knowledge of phylogeny and trait values for recent species. However, this approach has been rarely applied to study brain evolution so far. In this thesis, I focus on bats (Chiroptera). Bats are a suitable group for demonstrating the importance of brain size reductions. Considering their energetically demanding mode of locomotion, they are likely to have been under selection pressure for brain reduction. Furthermore, there is a large amount of data on body and brain mass of recent species available. Finally, phylogenetic relationships among bats are relatively well resolved. My present study is based on body masses and brain masses of 334 recent bat species (Baron et al., 1996) and on a phylogeny obtained by adjusting existing bat supertree (Jones et al., 2002) according to recent molecular studies. Analysing the data for...
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The Use of Bayesian Methods in Investment Decisions
Sosnovec, Jakub ; Bína, Vladislav (advisor) ; Váchová, Lucie (referee)
My bachelor thesis points at the application of Bayes methods during the decision making and moreover is interested in general types of investments and their advantages and disadvantages. The output of my thesis is the portfolio of materials used for three possible investments, specifically for gold investments, funds and agricultural lands during three economical conditions of the world - during recession, stagnation and growth. The model will be furthemore entered by expert's accurate estimation of possibilities that one or another condition of the world will happen. Apart from this, results will be compared with the variation of decision making during the uncertainty and thanks to this, we will demonstrate the difficulties of this method. My thesis ends with the presentation of methods which develop the process and specify the groundwork for decision making.
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Frequentist and Bayesian inference
Shykhmanter, Dmytro ; Vilikus, Ondřej (advisor) ; Hebák, Petr (referee)
The thesis provides both theoretical and practical comparison of frequentist and Bayesian methods of statistical inference. Comparing of these two concepts begins with describing the philosophy of probability theory. Also is introduced the problem of determinism as well as three main probability interpretations. Statistical inference is a process of making general conclusions based on a given evidence. The frequentist statistics uses the observed data as an only evidence for its conclusions, while the Bayesian one is based on an idea that the subjective degree of belief can be also used for these purposes. Why should one disregard to his experience, knowledge or even intuition? Often happens that results of statistical data analysis are useless in sense that they come out not as it is expected. This situation is illustrated when there are a number of ski resorts which are graded on five star scale. If we look to the top ten, we will find that some of those should not belong there, though the data says they do. Generally the top positions are occupied by the objects with fewer reviews, while those with more reviews get lower average score. Bayesian data analysis methods enable to eliminate this kind of problem. Based on a prior information about the whole data set, every ski resort would get a fair score and as the result, the model would better represent the quality of the each resort based on the respondents' reviews.
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