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Stochastic Programming Methods for Investment Decisions
Kubelka, Lukáš ; CFA, Tomáš Menčík, (referee) ; Popela, Pavel (advisor)
This thesis deals with methods of stochastic programming and their application in financial investment. Theoretical part is devoted to basic terms of mathematical optimization, stochastic programming and decision making under uncertainty. Furter, there are introduced basic principles of modern portfolio theory, substantial part is devoted to risk measurement techniques in the context of investment, mostly to the methods Value at Risk and Expected shortfall. Practical part aims to creation of optimization models with an emphasis to minimize investment risk. Created models deal with real data and they are solved in optimization software GAMS.
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Use of mathematical methods in creating an investment portfolio
Holub, Miroslav ; Novotná, Veronika (referee) ; Janková, Zuzana (advisor)
The bachelor thesis is focused on the use of mathematical methods in creating an investment portfolio, which is designed for small investor. The theoretical part of the thesis describes the necessary knowledge to understand Markowitz model, selected indicators of financial analysis and the Value at Risk method. The practical part contains a selection of investment instruments traded on the US market according to established criteria, the creation of a real portfolio of these investment instruments and the final evaluation of results.
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Value at Risk in R
ŽIŠKA, František
This thesis explores multiple methods of calculating currency risk with the use of value at risk, as well as implementing these methods in code language R. The first part of this thesis is theoretical and explains and proves three methods of assessing parametric and nonparametric models of value at risk and shows how precise they are and what disadvantagesthese models pose. The second part of this thesis focuses on implementing these value at risk calculation methods into code language R, resulting in code, which is able to calculate currency risk with these different value at risk methods using user input of needed values.
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Calculation of capital requirements of market risk for options on stock's basket
Lendacký, Peter ; Myška, Petr (advisor) ; Večeř, Jan (referee)
The goal of the paper is to compare different approach in calculation of capital requirement of market risk for options on stock's basket and describe their impact on selected instrument. The first part of the paper describes possible approaches for the capital requirement calculation, namely Standardized approach and Internal model approach, and the theoretical base for option pricing. An instrument with the embedded option on equities was chosen to show the impact. Although the instrument is valued using Monte Carlo simulation, one chapter is devoted to Black-Scholes model as the base model for option pricing. Powered by TCPDF (www.tcpdf.org)
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Quantitative methods in finance
Zboňáková, Lenka ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
In the present thesis we deal with the quantitative risk measures estimating the influence of market risk on the investments to the financial instruments. The most commonly used measure is Value at Risk which we introduce with its characteristics and modifications. Applying the methods to real data we deal with the problem of approximation of its distribution, especially in the multidimensional cases when the risk factors are dependent on each other. This leads us to explore copula functions that are in the thesis used to include the dependence structures of the risk factors to calculation of the risk measures. Chosen methods of approximation and evaluation of the risk measures are applied to real data and stated with outputs and their comparison.
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Estimations of risk with respect to monthly horizon based on the two-year time series
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Zichová, Jitka (referee)
The thesis describes commonly used measures of risk, such as volatility, Value at Risk (VaR) and Expected Shortfall (ES), and is tasked with creating models for measuring market risk. It is concerned with the risk over daily and over monthly horizons and shows the shortcomings of a square-root-of-time approach for converting VaR and ES between horizons. Parametric models, geometric Brownian motion (GBM) and GARCH process, and non-parametric models, historical simulation (HS) and some its possible improvements, are presented. The application of these mentioned models is demonstrated using real data. The accuracy of VaR models is proved through backtesting and the results are discussed. Part of this thesis is also a simulation study, which reveals the precision of VaR and ES estimates.
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Principal components analysis and its applications
Dubová, Mária ; Hendrych, Radek (advisor) ; Prášková, Zuzana (referee)
In the present thesis, we deal with the principal components analy- sis. In the first of this text, we study different aspects of principals components, for instance, their derivation for a multidimensional random vector from general distribution or their calculation based on a covariance or correlation matrix. It is also important to choose the proper number of principal components for reducing the dimensionality of data in order to preserve most of information. Theoretical knowledge are illustrated with several examples. In the second part of the thesis, we focus on the value at risk. This term is defined in the text also with seve- ral usual formulas to calculate it. Then, we deal with a practical application of this concept and the principal component analysis. Concretely, we analyse the portfolio of some different interest rates to obtain the value at risk in some cases. 1
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Advanced Techniques of Risk Aggregation
Dufek, Jaroslav ; Justová, Iva (advisor) ; Pešta, Michal (referee)
In last few years Value-at-Risk (Var) is a very popular and frequently used risk measure. Risk measure VaR is used in most of the financial institutions. VaR is popular thanks to its simple interpretation and simple valuation. Valuation of VaR is a problem if we assume a few dependent risks. So VaR is estimated in a practice. In presented thesis we study theory of stochastic bounding. Using this theory we obtain bounds for VaR of sum a few dependent risks. In next part of presented thesis we show how we can generalize obtained bounds by theory of copulae. Then we show numerical algorithm, which we can use to evaluate bounds, when exact analytical evaluate isn't possible. In a final part of presented thesis we show our results on practical examples.
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Use of mathematical methods in creating an investment portfolio
Holub, Miroslav ; Novotná, Veronika (referee) ; Janková, Zuzana (advisor)
The bachelor thesis is focused on the use of mathematical methods in creating an investment portfolio, which is designed for small investor. The theoretical part of the thesis describes the necessary knowledge to understand Markowitz model, selected indicators of financial analysis and the Value at Risk method. The practical part contains a selection of investment instruments traded on the US market according to established criteria, the creation of a real portfolio of these investment instruments and the final evaluation of results.
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