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Interest Rate Risk Analysis by Principal Component Method
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Prášková, Zuzana (referee)
Presented study analyzes interest rate risk associated with the possession of given fixed coupon bond. In the first chapter, we define some of the basic concepts and provide description of available data. These are historical data on spot interest rates of zero-coupon bonds for various times to maturity which will be used for the construction of the yield curves. Based on these bond yield curves we evaluate the bond, thus obtaining a picture of the evolution of its price. Later on, we try to estimate its price tomorrow. We present two approaches how to deal with this problem. First approach is the normal interest rate risk analysis based on duration and convexity, second approach is the method of principal components which will be applied to the historical daily changes in yield curves. The method of principal components is introduced in detail.
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Convexity in chance constraints programming
Olos, Marek ; Kopa, Miloš (advisor) ; Adam, Lukáš (referee)
1 Abstract: This thesis deals with chance constrained stochastic programming problems. We consider several chance constrained models and we focus on their convexity property. The thesis presents the theory of α-concave functions and measures as a basic tool for proving the convexity of the problems. We use the results of the theory to prove the convexity of the models first for the continu- ous distributions, then for the discrete distributions of the random vectors. We characterize a large class of the continuous distributions, that satisfy the suffi- cient conditions for the convexity of the given models and we present solving algorithms for these models. We present sufficient conditions for the convexity of the problems with dicrete distributions, too. We also deal with the algorithms for solving non-convex problems and briefly discuss the difficulties that can occur when using these methods.
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Convexity in chance constraints programming
Olos, Marek ; Kopa, Miloš (advisor) ; Adam, Lukáš (referee)
This thesis deals with chance constrained stochastic programming pro- blems. The first chapter is an introduction. We formulate several stochastic pro- gramming problems in the second chapter. In chapter 3 we present the theory of α-concave functions and measures as a basic tool for proving convexity of the problems formulated in chapter 2 for the continuous distributions of the random vectors. We use the results of the theory to characterize a large class of the conti- nuous distributions, that satisfy the sufficient conditions for the convexity and to prove convexity of concrete sets. In chapter 4 we present sufficient conditions for the convexity of the problems and we briefly discuss the method of the p-level ef- ficient points. In chapter 5 we solve a portfolio selection problem using Kataoka's model. 1
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Gradient polyconvexity and its application to problems of mathematical elasticity and plasticity
Zeman, Jiří ; Kružík, Martin (advisor) ; Zeman, Jan (referee)
Polyconvexity is a standard assumption on hyperelastic stored energy densities which, together with some growth conditions, ensures the weak lower semicontinuity of the respective energy functional. The present work first reviews known results about gradient polyconvexity, introduced by Benešová, Kružík and Schlömerkemper in 2017. It is an alternative property to polyconvexity, better-suited e.g. for the modelling of shape-memory alloys. The principal result of this thesis is the extension of an elastic material model with gradient polyconvex energy functional to an elastoplastic body and proving the existence of an energetic solution to an associated rate- independent evolution problem, proceeding from previous work of Mielke, Francfort and Mainik. 1
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Maximum likelihood theory for not i.i.d. observations
Kielkowská, Eva ; Omelka, Marek (advisor) ; Pešta, Michal (referee)
Maximum likelihood approach for independent but not identically distributed observations is studied. In the first part of the thesis, conditions for consistency and asymptotic normality of the maximum likelihood estimates for this case are stated. Uniform integrability has a major role in proving the desired properties. K-sample problem serves as an example for using the described method. The second part is focused on estimates obtained by minimizing convex functions. Convexity is a key for showing the consistency and asymptotic normality of the estimates in this case. The results can be used for maximum likelihood when observations with logconcave densities are involved. Finally, normal linear model, logistic regression and Poisson regression examples are provided to present the application of the method.
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Convexity in chance constraints programming
Olos, Marek ; Kopa, Miloš (advisor) ; Adam, Lukáš (referee)
This thesis deals with chance constrained stochastic programming pro- blems. The first chapter is an introduction. We formulate several stochastic pro- gramming problems in the second chapter. In chapter 3 we present the theory of α-concave functions and measures as a basic tool for proving convexity of the problems formulated in chapter 2 for the continuous distributions of the random vectors. We use the results of the theory to characterize a large class of the conti- nuous distributions, that satisfy the sufficient conditions for the convexity and to prove convexity of concrete sets. In chapter 4 we present sufficient conditions for the convexity of the problems and we briefly discuss the method of the p-level ef- ficient points. In chapter 5 we solve a portfolio selection problem using Kataoka's model. 1
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Interest Rate Risk Analysis by Principal Component Method
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Prášková, Zuzana (referee)
Presented study analyzes interest rate risk associated with the possession of given fixed coupon bond. In the first chapter, we define some of the basic concepts and provide description of available data. These are historical data on spot interest rates of zero-coupon bonds for various times to maturity which will be used for the construction of the yield curves. Based on these bond yield curves we evaluate the bond, thus obtaining a picture of the evolution of its price. Later on, we try to estimate its price tomorrow. We present two approaches how to deal with this problem. First approach is the normal interest rate risk analysis based on duration and convexity, second approach is the method of principal components which will be applied to the historical daily changes in yield curves. The method of principal components is introduced in detail.
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Convexity in chance constraints programming
Olos, Marek ; Kopa, Miloš (advisor) ; Adam, Lukáš (referee)
1 Abstract: This thesis deals with chance constrained stochastic programming problems. We consider several chance constrained models and we focus on their convexity property. The thesis presents the theory of α-concave functions and measures as a basic tool for proving the convexity of the problems. We use the results of the theory to prove the convexity of the models first for the continu- ous distributions, then for the discrete distributions of the random vectors. We characterize a large class of the continuous distributions, that satisfy the suffi- cient conditions for the convexity of the given models and we present solving algorithms for these models. We present sufficient conditions for the convexity of the problems with dicrete distributions, too. We also deal with the algorithms for solving non-convex problems and briefly discuss the difficulties that can occur when using these methods.
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Behavior of bonds conditioned by negative interest rates
Biljakov, Nik ; Stádník, Bohumil (advisor) ; Galuška, Jiří (referee)
Current economic situation is characterized for deflation and low inflation, low economic growth, and low or negative interest rates, which lead to phenomenon of issuing governments bonds with negative yield. The main goal of this work is to understand the valuation and behavior of bonds with condition of negative interest rates, analyze impacts of negative rates on volatility of bonds. This work also compares the behavior of negative yields of bonds in contrast with positive yields. The contribution of this work consists in the critical evaluation of limitations of the formula for calculating the bond price to fulfill its role if the values of negative interest rates are too low.
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Bond valuation theory
Krchňavý, Martin ; Čech, Tomáš (advisor) ; Pracný, Jakub (referee)
The bachelor thesis discusses the theory of bond valuation with a focus on traditional coupon and zero-coupon bonds without embedded options. Introduction specifies author's objectives and methods, which are used to fulfil these objectives. Theoretical part explains the concept of bond and analyses its individual attributes, such as price, yield and risk. The part with the practical application of the theory contains the description of data obtained from Thomson Reuters Eikon trading platform followed by the demonstration of yield and risk measurements and the valuation of my exemplary bond, which is Czech sovereign bond with a fixed coupon rate issued in the national currency. Conclusion evaluates the achievement of objectives and the potential utilization of results in praxis.
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