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Information Extraction of Probability and Risk of Returns using Options Prices
Cícha, Martin ; Trešl, Jiří (advisor) ; Cipra, Tomáš (referee) ; Málek, Jiří (referee)
The issue of forecasting the future price of risky financial assets has attracted academia and business practice since the inception of the stock exchange. Also due to the just finished financial crisis, which was the worst crisis since the Great Depression, it is clear that research in this area has not been finished yet. On the contrary, new challenges have been raised. The main goal of the thesis is the demonstration of the significant information potential which is hidden in option market prices. These prices contain informations on probability distribution of the underlying asset returns and the risk connected with these returns. Other objectives of the thesis are the forecast of the underlying asset price distribution using parametric and nonparametric estimates, the improvement of this forecast using the utility function of the representative investor, the description of the current market sentiment and the determination of the risk premium, especially the risk premium on Czech market. The thesis deals with the forecast of the underlying asset price probability distribution implied by the current option market prices using parametric and nonparametric estimates. The resulting distribution is described by the moment characteristics which represent a valuable tool for analyzing the current market sentiment. According to the theory, the probability distribution of the underlying asset price implied by option prices is risk neutral, i.e. it applies only to risk neutral investors. The theory further implies that the distribution of real world can be derived from the risk neutral distribution using utility function of the representative investor. The inclusion of a utility function of representative investor improves the forecast of the underlying asset price distribution. Three different utility functions of traditional risk theory are used in the thesis. These functions range from the simple power function to the general function of hyperbolic absolute risk aversion (HARA). Further, Friedman-Savage utility function is used. This function allows both a risk averse investor and a risk loving investor. The thesis also answers the question: Are the current asset prices at so high level that the purchase of the asset means a gamble? The risk premium associated with investing in the risky asset is derived in the thesis. The risk premium can be understood as the premium demanded by investors for investment in a risky asset against the investment in a riskless asset. All the theoretical methods introduced in the thesis are demonstrated on real data coming from two different markets. Developing market is represented by shares of CEZ and developed market is represented by S&P 500 futures. The thesis deals with demonstrations in single point in time as well as in available history of the data. The forecasts of the underlying asset price distribution and the relating risk premium are constructed in the available data history. The goals and the objectives of the thesis have been achieved. The contribution of the thesis is the development of parametric and nonparametric methodology for estimating the underlying asset price probability distribution implied by the option market prices so that the nature of the particular market and instrument is captured. The further contribution of the thesis is the construction of the forecasts of the underlying asset price distribution and the construction of the market sentiment in the available history of data. The contribution of the thesis is also the construction of the market risk premium in the available history and the establishment of the hypothesis that the markets gamble before the crisis.
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Approaches to Functional Data Clustering
Pešout, Pavel ; Marek, Luboš (advisor) ; Trešl, Jiří (referee) ; Palát, Milan (referee)
Classification is a very common task in information processing and important problem in many sectors of science and industry. In the case of data measured as a function of a dependent variable such as time, the most used algorithms may not pattern each of the individual shapes properly, because they are interested only in the choiced measurements. For the reason, the presented paper focuses on the specific techniques that directly address the curve clustering problem and classifying new individuals. The main goal of this work is to develop alternative methodologies through the extension to various statistical approaches, consolidate already established algorithms, expose their modified forms fitted to demands of clustering issue and compare some efficient curve clustering methods thanks to reported extensive simulated data experiments. Last but not least is made, for the sake of executed experiments, comprehensive confrontation of effectual utility. Proposed clustering algorithms are based on two principles. Firstly, it is presumed that the set of trajectories may be probabilistic modelled as sequences of points generated from a finite mixture model consisting of regression components and hence the density-based clustering methods using the Maximum Likehood Estimation are investigated to recognize the most homogenous partitioning. Attention is paid to both the Maximum Likehood Approach, which assumes the cluster memberships to be some of the model parameters, and the probabilistic model with the iterative Expectation-Maximization algorithm, that assumes them to be random variables. To deal with the hidden data problem both Gaussian and less conventional gamma mixtures are comprehended with arranging for use in two dimensions. To cope with data with high variability within each subpopulation it is introduced two-level random effects regression mixture with the ability to let an individual vary from the template for its group. Secondly, it is taken advantage of well known K-Means algorithm applied to the estimated regression coefficients, though. The task of the optimal data fitting is devoted, because K-Means is not invariant to linear transformations. In order to overcome this problem it is suggested integrating clustering issue with the Markov Chain Monte Carlo approaches. What is more, this paper is concerned in functional discriminant analysis including linear and quadratic scores and their modified probabilistic forms by using random mixtures. Alike in K-Means it is shown how to apply Fisher's method of canonical scores to the regression coefficients. Experiments of simulated datasets are made that demonstrate the performance of all mentioned methods and enable to choose those with the most result and time efficiency. Considerable boon is the facture of new advisable application advances. Implementation is processed in Mathematica 4.0. Finally, the possibilities offered by the development of curve clustering algorithms in vast research areas of modern science are examined, like neurology, genome studies, speech and image recognition systems, and future investigation with incorporation with ubiquitous computing is not forbidden. Utility in economy is illustrated with executed application in claims analysis of some life insurance products. The goals of the thesis have been achieved.
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Hurst Exponent and Randomness in Time Series
Zeman, Martin ; Trešl, Jiří (advisor) ; Hušek, Roman (referee)
The main goal of this thesis is to test the ability of the Hurst exponent to recognise some processes with deterministic signal as nonrandom and to test the randomness of daily stock returns of three stocks traded in BCPP. Critical values to determine the critical region of a randomness hypothesis test were set for this purpose. Another goal of the thesis is the description of the Hurst exponent estimation by means of Rescaled Range Analysis and outline some problems accompanying this estimation if the Hurst exponent would be used as a randomness indicator. Within the frame of Rescaled Range Analysis was constructed another method that showed to be successful in recognising some series that contain deterministic signal.
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Application of technical analysis indicators on a market data
Tabiš, Peter ; Trešl, Jiří (advisor) ; Bašta, Milan (referee)
The purpose of the thesis is test of current technical analysis indicators with the support of basic statistical software (Excel and PASW STATISTICS). During the test we will apply the correlation process in order to find two less similar markets. Subsequently, we will use these markets for testing the individual indicators of the analysis. The chosen indicators are those of the highest popularity as far as the profit/loss analysis is considered.
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Analysis of selected commodities from investor's point of view
Škultéty, Daniel ; Trešl, Jiří (advisor) ; Václavík, Tomáš (referee)
The purpose of this thesis is to analyze investment options into wheat, corn and rice futures throughout different time horizons. Mostly we use daily closing prices for the last fifteen years. General knowledge of the field in context of nowadays is required to perform such an analysis. To achieve our goals we use technical analysis, time series analysis and we discuss the fundaments of price movements. Contribution of this thesis can be summed as presenting the basic tools of technical analysis in real world, presenting the fundamentals of price movements in one place and practical application of time series analysis on futures prices. By doing so we can confirm that random walk thesis is not unsubstantial but cannot be generalized for all instruments and periods of capital market.
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Application of R/S Analysis at Financial Markets
Vilhanová, Vanda ; Trešl, Jiří (advisor) ; Kodera, Jan (referee)
The aim of this graduation thesis is the descriptiton of R/S analysis and it's aplication on chosen time series of share prices and exchange rates. Some main models of financial time series will be mentioned in the second chapter. There will described basic linear models of stationary and non stationary time series and models of volatility. Then we will focus on the main theme of this thesis, R/S analysis. The algorithm of R/S analysis and the interpretation of the Hurst exponent will be described in the forth chapter. In the fifth chapter, the R/S analysis will by applied on real data sets. There will be two data sest of share prices of Telefónica O2 and Philip Morris and two data sets of exchange rates CZK/EUR and CZK/USD. The results will be interpreted and compared.
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Technical analysis of selected investment instrument
Gronský, Andrej ; Trešl, Jiří (advisor) ; Veselá, Jitka (referee)
The principal aim of this graduation thesis is to characterize technical analysis including its application to chosen investment instrument. The begining of the thesis consists of the main investment approaches in the capital markets and their comparison with technical analysis. Afterwards, the definition and targets of technical analysis are given. Further, the work focuses on the Dow Theory as the main basis of the contemporary technical analysis and mentions other approaches in technical analysis. Then, the instruments of technical analysis are introduced. Graphical methods are only outlined whereas technical indicators are the focus of attention. There is the selection of twelve of them including their construction and usage. Finally, the application of chosen technical indicators belonging to chosen financial instrument is given and achieved results are commented.
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