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Use of Interest Rate Models for Interest Rate Risk Management in the Czech Financial Market Environment
Cíchová Králová, Dana ; Arlt, Josef (advisor) ; Cipra, Tomáš (referee) ; Witzany, Jiří (referee)
The main goal of this thesis is to suggest an appropriate approach to interest rate risk modeling in the Czech financial market environment in various situations. Three distinct periods are analyzed. These periods, which are the period before the global financial crisis, period during the financial crisis and in the aftermath of the global financial crisis and calming subsequent debt crisis in the eurozone, are characterized by different evaluation of liquidity and credit risk, different relationship between financial variables and market participants and different degree of market regulations. Within this goal, an application of the BGM model in the Czech financial market environment is crucial. Use of the BGM model for the purpose of predicting a dynamics of a yield curve is not very common. This is firstly due to the fact that primary use of this model is a valuation of interest rate derivatives while ensuring the absence of arbitrage and secondly its application is relatively difficult. Nevertheless, I apply the BGM model to obtain predictions of the probability distributions of interest rates in the Czech and eurozone market environment, because its complexity, direct modeling of a yield curve based on market rates and especially a possibility of parameter estimation based on current swaptions volatilities quotations may lead to a significant improvement of predictions. This improvement was also confirmed in this thesis. Use of swaptions volatilities market quotations is especially useful in the period of unprecedented mone- tary easing and increased number of central banks and other regulators interventions into financial markets that occur after the financial crisis, because it reflects current market expectations which also include future interventions. As a consequence of underdevelopment of the Czech financial market there are no market quotations of Czech koruna denominated swaptions volatilities. I suggest their approximations based on quotations of euro denominated swaptions volatilities and also using volatilities of koruna and euro forward rates. Use of this approach ensures that predictions of the Czech yield curve dynamics contain current market expectations. To my knowledge, any other author has not presented similar application of the BGM model in the Czech financial market environment. In this thesis I further predict a Czech and Euro area money market yield curve dynamics using the CIR and the GP models as representatives of various types of interest rates models to compare these predictions with BGM predictions. I suggest a comprehensive system of three criteria, based on comparison of predicti- ons with reality, to describe a predictive power of selected models and an appropria- teness of their use in the Czech market environment during different situations in the market. This analysis shows that predictions of the Czech money market yield curve dynamics based on the BGM model demonstrate high predictive power and the best 8 quality in comparison with other models. GP model also produces relatively good qua- lity predictions. Conversely, predictions based on the CIR model as a representative of short rate model family completely failed when describing reality. In a situation when the economy allows negative rates and there is simultaneously a significant likelihood of their implementation, I recommend to obtain predictions of Czech money market yield curve dynamics using GP model which allows existence of negative interest rates. This analysis also contains a statistical test for validating the predictive power of each model and information on other tests. Berkowitz test rejects a hypothesis of accurate predictions for each model. However, this fact is common in real data testing even when using relatively good model. This fact is especially caused by difficult fulfilment of test conditions in real world. To my knowledge, such an analysis of the predictive power of selected interest rate models moreover in the Czech financial market environment has not been published yet. The last goal of this thesis is to suggest an appropriate approach to obtaining pre- dictions of Czech government bonds risk premium dynamics. I define this risk premium as a difference between government bond yields and fixed rate of CZK IRS with the same length. I apply the GP model to describe the dynamics of this indicator of the Czech Republic credit risk. In order to obtain a time series of the risk premium which are necessary for estimation of GP model parameters I firstly estimate yield curves of Czech government bonds using Svensson model for each trading day since 2005. Resulting si- mulations of risk premium show that the GP model predicts the real development of risk premiums of all maturities relatively well. Hence, the proposed approach is suitable for modeling of Czech Republic credit risk based on the use of information extracted from financial markets. I have not registered proposed approach to risk premium modeling moreover in the Czech financial market environment in other publications.
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Solving of partial differential equations by Fourier method
Barvenčík, Oldřich ; Opluštil, Zdeněk (referee) ; Nechvátal, Luděk (advisor)
Bachelor thesis is a survey text which deals with solving partial deferential equations by Fourier method, i.e. method when we look for a solution of (initial) boundary value problem in form of the infinite Fourier series. The key step is a hypothesis that the solution can be expressed in form with separated variables, therefore the method is sometimes called separation of variables method. The essence can be demonstrated on parabolic and hyperbolic homogeneous problems. In the thesis both types in one (space) dimension are systematically analyzed, at first homogeneous problem, then homogeneous one with non-homogeneous boundary conditions and finally completely non-homogeneous problem.
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The trans-fatty acids in subcutaneous fat and in fat content of breast milk as an indicator of their nutritional intake
Dlouhý, Pavel ; Anděl, Michal (advisor) ; Dostálová, Jana (referee) ; Hrubý, Stanislav (referee) ; Zadák, Zdeněk (referee)
Trans fatty acids (TFA) are unsaturated fatty acids, which have one or more double bonds in the trans configuration. Their main dietary sources are partially hardened fats and food products containing partially hardened fats (margarines, shortenings, bakery products, and fast foods). TFA are thought to increase the risk of coronary heart disease and type 2 diabetes. These fatty acids have adverse effects on blood lipid levels, increasing LDL-cholesterol while decreasing HDL-cholesterol. Consumption of TFA can also impair insulin sensitivity. High intake of TFA is associated with systemic inflammation, activation of immune functions and endothelial dysfunction. Hypotheses also exist that TFA may have adverse effect on the metabolism of essential fatty acids and foetus development. The concentration of TFAs in subcutaneous fat is a very good indicator of dietary exposure of TFA. This concentration reflects long-term dietary intake of these fatty acids. Levels of TFA in human milk are more variable; however, it is quite simple to obtain a sample of human milk. The purpose of our studies was to determine (a) content of TFA in subcutaneous fat samples from persons with coronary atherosclerosis and from persons with no sign of coronary dinase and (b) the content of TFA in early human milk of breast-feeding women...
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Population genetic analysis of Old Kladruber horse
Vostrá Vydrová, Hana ; Majzlík, Ivan (advisor) ; Karel, Karel (referee)
The Old Kladruber horse, along with the Lipizzaner horse, Andalusian horse and Lusitano horse, is of the original Italo-Spanish type. The Old Kladruber horse is kept in two colour varieties (grey and black). Because the population is closed, there is a concern about the loss of genetic variation. The genetic diversity and population structure were analysed in the Old Kladruber horse breed based on the pedigree information of animals that were registered in the Studbook to identify factors that may have affected the genetic variability of the breed. Pedigree records collected from 1729 to 2013 contained information on 7971 animals that were used in the analyses. The pedigree depth was up to 33 generations, with an average of 15.1 complete generations. The effective number of founders and ancestors contributing to the current genetic pool was 92.69 and 17.16, respectively. The average values of the inbreeding coefficient were as follows: 13% (with a maximum value of 29%) for the reference population (individuals that can currently take part in reproduction, n=612), 11% for the grey variety (with a maximum value of 25%) and 15% for the black variety (with a maximum value of 29%). The proportion of inbred animals was high (99%). The average rate of inbreeding in the reference population was 1%: 0.8% for the grey variety and 1.1% for the black variety, and the respective estimates of the effective population sizes were 52 for the reference population, 62 for the grey variety and 45 for the black variety. The estimated percentage of genetic diversity lost due to non-random mating within subpopulations and the reference population was 1.0, 1.0 and 1.2%, respectively. The total loss of genetic diversity in the reference population, in the grey variety and in the black variety was 11%, 13% and 17%, respectively.
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The Selected Stochastic Programs in Engineering Design
Čajánek, Michal ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
Two-stage stochastic programming problem with PDE constraint, specially elliptic equation is formulated. The computational scheme is proposed, whereas the emphasis is put on approximation techniques. We introduce method of approximation of random variables of stochastic problem and utilize suitable numerical methods, finite difference method first, then finite element method. There is also formulated a mathematical programming problem describing a membrane deflection with random load. It is followed by determination of the acceptableness of using stochastic optimization rather than deterministic problem and assess the quality of approximations based on Monte Carlo simulation method and the theory of interval estimates. The resulting mathematical models are implemented and solved in the general algebraic modeling system GAMS. Graphical and numerical results are presented.
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Impact of horizontal and vertical pattern of habitats on birds diversity
Schovánková, Hana ; Šímová, Petra (advisor) ; Moudrý, Vítězslav (referee)
This diploma thesis follows up the influence of horizontal and vertical structure of biotopes on biodiversity of bird species of Czech Republic of forest and open sites. Vertical structure model was created from digital model of surface of Czech Republic (1st generation) and digital model of relief of Czech Republic (5th generation). Information about horizontal structure were derived by analyzing aerial imagery. Then single variables were detected from these data. Subsequently, it was analyzed which of these variables and which way influence bird diversity. On both types of sites was found increasing bird diversity with increasing diversity of vertical structure. With increasing horizontal structure, however, bird diversity significantly increased only on open sites. The influence of other characteristics was mostly different on bird diversity of open and forest sites, but, for both types of sites, the positive influence had for example edge density of land cover categories or edge density of height categories. Additional part of this thesis was to explore if vertical characteristics of biotopes could influence prediction of selected bird species. Results was different in forest and open biotopes, nevertheless in both types of sites was found potential use of both horizontal and vertical variables.
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Vliv velikosti a krytí holiny na odrůstání douglasky tisolisté
Ludvík, Ladislav
The aim of this thesis was to determine what influence the varying size of clearing and cover of the stand has on the gradual growth of Douglas fir (Pseudotsuga menziesii /Mirb./ Franco). The evaluation of different types of planting material (2 + 1, 2 + 2, 3 + 0 and f1 + k1) on partially covered locations is part of the thesis as well. Examination was conducted on research locations ÚZPL established in year 2010 (17 locations) and 2011 (4 locations) in the forests owned by the city of Brno. The survey was conducted after the end of the vegetation period in the months of September and November of the year 2013. It is a follow-up survey of the previous measurements realized in the fall of 2012. On all locations at least 100 individuals were measured and evaluated. These are the variables and signs assessed -- the overall size of the above ground part (in years 2012 and 2013), quantity of growth in each year, the thickness of the root neck, number of plants with multitude stems, the deviation of stem (straight, up to three times the diameter of the stem and more than three times diameter of the stem), the shape of the tree-top (triangle, ellipsoid, round and one-sided) the length of needles, the colour of the assimilatory part (green, bright green and yellow), loss percentage. These results were confronted with results from previous years. The results of this master thesis proved, that different size (and cover) of clearing and the used planting material have influence on the successful planting and growth of Douglas fir cultivation. The Douglas fir seems to be growing more successfully on locations protected at least from three sides where the width of clearing is no more than 35 metres. If quality planting material is used, low mortality of the plants can be expected as well. Aproximately after three years the quantity of growth and the thickness of the root neck on different locations start to match. On the locations protected from two sides and with the distance of the clearing from the stand not above the 1,5 multiple of the stand height, the covered-root plants (f1 + K1) and plant type 2+1 was proved to be most successful in growth and suffered from minimal loss even after three vegetation periods. The losses which occurred in 2013 were comparably lower to those in 2012.
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Winter Density of House Sparrow in Different types of Rural Settlements along the Czech – Austria Border
Oberpfalzerová, Michaela ; Zasadil, Petr (advisor) ; Šmejdová, Lucie (referee)
From the point of view of the Czech Republic in the last 80 years we can specify two periods, which had a significant impact on the general character and development in agriculture. The first period can be traced to the 50s of the last century, in which the concentration of agricultural production headed towards to factory farming. The second one began at the beginning of the 90s. At that time a sharp downtown of animal production occurred and the sooner concentrated production began, after the regaining by previous owners, to erode into what it is today private agriculture.
This thesis aims tocontribute to a confirmation of rejection of the hypothesis that the above described changes have a negative impact on the selected avian species. These species are represented by significantsynanthropic birds: house sparrow (which is a crucial representative in this thesis), tree sparrow and collared dove. Thirty municipalities were chosen to emphasize the differences in quantity of these species, half of them located on each side of the border with the Czech Republic and Austria. The comparison of quantities of bird populations took place in the surroundings of the cities Znojmo and Retz.In this thesis the Republic of Austria acts as a country which has not been burdened by a substantial economic development and which has applied the continuous market economy since the end of the Second World War.
In the individual squares the numbers of the representatives of the studied species and the environmental characteristics were recorded during the winter period. The significant differences in the numbers of birds at selected locations were demonstrated using a multifactor ANOVA STATISTICA 12. Moreover, the impact of selected environmental variables on the abundance of observed species was also analysed. It was found that the selected species depend on an inclusion into the individual states as well as on a classification into various biotope types. Finally, the dependence on the area of trees and bushes, the proportion of new buildings and the presence of poultry in the square were also observed. The most numerous species in the Republic of Austria was the house sparrow, the most abundant species in the Czech Republic was the collared dove. A slight increase in the occurrence of the collared dove was recorded in both states. Tree sparrow as a species occurred in relatively large numbers, but only locally. It was found that the populationsof the above mentioned species were generally more numerous in the Austrian municipalities. An interesting fact is that most of the observed individuals in the Czech Republic occurred in village built-up areas rather than in agricultural premises, as it was initially estimated.
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