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Are financial returns and volatility multifractal at all?
Sedlaříková, Jana ; Krištoufek, Ladislav (advisor) ; Kraicová, Lucie (referee)
Over the last decades, multifractality has become a downright stylized fact in financial markets. However, its presence has not been adequately statistically proved. The main aim of this thesis is to contribute to the discussion by an ex- tensive statistical analysis of the problem. We investigate returns and volatility of the collection of the four stock indices employing the three popular methods: the GHE, the MF-DFA, and the MF-DMA method. By comparing the results of the original series to those for simulated monofractal series, we conclude that stock market returns as well as volatility exhibit a multifractal nature. Additionally, in order to understand the origin of underlying multifractality, we study vari- ous surrogate series. We found that a fat-tailed distribution significantly affects multifractality. On the other, we were not able to confirm the impact of time correlations as the results strongly depend on the applied model. JEL Classification F12, G02, G10, C12, C22, C49, C58 Keywords econophysics, multifractality, financial markets, Hurst exponent Author's e-mail jana.sedlarikova@gmail.com Supervisor's e-mail kristoufek@ies-prague.org
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Backtesting of Different Scaling Rules for Value at Risk in the Basel Context
Klečka, Adam ; Krištoufek, Ladislav (advisor) ; Avdulaj, Krenar (referee)
1 Abstract There is a discrepancy between two important horizon for Value at Risk modelling in the Basel context. We take 10-day values for determining the regulatory capital but we consider 1-day models for backtesting. The main objective of this thesis is to examine the suitability of the currently used Square Root of Time rule for Value at Risk scaling. We compare its performance with the method utilizing Hurst exponent. Our analysis is performed for both the normal and stable distribution. We conclude that the normality assumption and the Square Root of Time rule prevail under the regulatory parameters. The results of the Hurst exponent method are not favourable under normality. On the other hand, the performance for the stable distribution is quite satisfactory under non-Basel parameters and the Hurst exponent complements this distribution very well. Therefore, the use of stable distribution and the Hurst exponent method is justified when dealing with complex non-linear instruments, during turbulent periods, or for general non-Basel setting. In general however, our results are strongly data-dependent and further evidence is needed for any conclusive implications. JEL Classification G21, G28, C58, G32, C14, G18 Keywords value at risk, backtesting, volatility scaling, Basel II, stable distribution, Hurst...
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Multifractal Analysis of Stock Market Prices
Čechová, Kristýna ; Krištoufek, Ladislav (advisor) ; Vošvrda, Miloslav (referee)
The aim of this thesis is to provide an empirical evidence of multifractality in financial time series and to discuss the relevance of this concept for the current financial theory. We have applied two methods, the Multifractal Detrended Fluctuation analysis and the Generalized Hurst exponent method, on components of the Dow Jones Industrial Average. We analyzed daily data of 30 companies traded on U.S. stock markets from 2002 to 2012. We present results supporting presence of multiscaling in open-close returns. Contrary to published literature, we were not able to find any significant multiscaling in volatility. Moreover based on our analysis, multiscaling is not present in standardized returns and as multifractality requires relatively complicated models, this is our most valuable result. 1
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Fundamental and technical analysis of a particular asset
Nepomnyashchiy, Ilya ; Fičura, Milan (advisor) ; Mazáček, David (referee)
The goal of the thesis is to evaluate the degree of efficiency of the particular markets and to apply the methods of fundamental and technical analysis on them in order to assess their efficiency in terms of profitablity. The thesis analyses the degree of long-term memory of the particular commodities and stock indices via Hurst coefficient. Afterwards fundamental and technical methods are applied to the market with the highest degree of long-term memory, which is the feeder cattle market. Indidivual methods from both disciplines are being applied at first, after wich a combnation of both is appleid as well. The result is the discovery, whether combining the two approaches leads to a higher profitability of the trading strategy. At the end the effect of transacton costs is also evalauted and a final conclusion is made regarding the profit potential of both methods for the case of individual Czech investor.
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Clouds and Hills Generation Using Fractal Geometry
Tůma, Petr ; Zuzaňák, Jiří (referee) ; Venera, Jiří (advisor)
This work is concerned with generation of landscape objects using fractal geometry. In this work is explained what the fractal is and terms associated with them. The other parts describe basic theoretical ideas and implementation of these algorithms. The Capital theme is generation of models clouds and hills in values of input parameters, their presentation and date media saved there. The project includes my algorithm extension for hills generation of course. At the conclusion of this work are summarized tendencies of next development and my results.
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Analysis and Prediction of Foreign Exchange Markets by Chaotic Attractors and Neural Networks
Pekárek, Jan ; Dostál, Petr (referee) ; Budík, Jan (advisor)
This thesis deals with a complex analysis and prediction of foreign exchange markets. It uses advanced artificial intelligence methods, namely neural networks and chaos theory. It introduces unconventional approaches and methods of each of these areas, compares them and uses on a real problem. The core of this thesis is a comparison of several prediction models based on completely different principles and underlying theories. The outcome is then a selection of the most appropriate prediction model called NAR + H. The model is evaluated according to several criteria, the pros and cons are discussed and approximate expected profitability and risk are calculated. All analytical, prediction and partial algorithms are implemented in Matlab development environment and form a unified library of all used functions and scripts. It also may be considered as a secondary main outcome of the thesis.
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The Use of Artificial Intelligence on Stock Market
Barjak, Maroš ; Budík, Jan (referee) ; Dostál, Petr (advisor)
The thesis deals with design, implementation and optimization of a model based on artificial intelligence and neural networks, which is able to predict future time series prices on a stock market. Main goal is to create an object oriented application for successful future trend prediction of financial derivatives with the use of cooperating methods such as Hurst exponent evaluation and automated market simulation.
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Capital Asset Price Modelling: Concept VAPM
Kuklik, Robert G. ; Janda, Karel (advisor) ; Kodera, Jan (referee) ; Lukáš, Ladislav (referee)
The key objective of this thesis is the outline of an alternative capital market modeling framework, the Volatility Asset Pricing Model, VAPM, inspired by the innovative dual approach of Mandelbrot and Hudson using the method based on synthesis of two seemingly antagonistic factors -- the volatility of market prices and their serial dependence determining the capital markets' dynamics. The pilot tests of this model in various periods using the market index as well as a portfolio of selected securities delivered generally satisfactory results. Firstly, the work delivers a brief recapitulation regarding the concepts of a consumer/investor choice under general conditions of hypothetical certainty. Secondly, this outline is then followed by a description of the "classical" methodologies in the risky environment of uncertainty, with assessment of their corresponding key models, i.e. the CAPM, SIM, MIM, APTM, etc., notwithstanding results of the related testing approaches. Thirdly, this assessment is based on evaluation of the underlying doctrine of Efficient Market Hypothesis in relation to the so called Random Walk Model. Fourthly, in this context the work also offers a brief exposure to a few selected tests of these contraversial concepts. Fifthly, the main points of conteporary approaches such as the Fractal Dimension and the Hurst Exponent in the dynamic framework of information entropy are subsequently described as the theoretical tools leading to development of the abovementioned model VAPM. The major contribution of this thesis is considered its attempt to apply the abovementioned concepts in practice, with the intention to possibly inspire a further analytical research.
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