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Fish wars : dynamic externality in fishing
Fiala, Tomáš ; Vošvrda, Miloslav (referee) ; Gregor, Martin (advisor)
The dramatic state of world fish stock is often attributed to the open-access nature of fishing grounds. In this thesis we investigate the consequences of unrestricted access to fisheries by adopting game theoretic framework. We describe the situation of fish appropriation by dynamic model and find some of its Nash equilibria. We show that one of the possible results of the nonexclusive nature of fisheries is overexploitation. Moreover, we find that other outcomes are possible as well. The tragedy of commons is, thus, not inevitable.
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Robust Estimator of Persistence in Financial Time Series
Jeřábek, Jakub ; Hanzák, Tomáš (referee) ; Vošvrda, Miloslav (advisor)
The goal of this thesis is to develop a novel robust log-periodogram regression method to detect the presence of long memory in time series. By the use of the Least Trimmed Squares regression we obtain an estimator that is less sensitive to outliers and leverage points, which is highly desirable particularly because the Periodogram estimator itself is prone to such inhomogeneities. In a Monte Carlo study, the new estimator provides smaller bias than the classical Least Squares log-Periodogram estimator. On the other hand the variability of estimation is increased. The proposed estimator is compared to existing long memory estimators on a case study of international currency exchange rates.
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Pricing of gas swing options
Pokorná, Andrea ; Janda, Karel (advisor) ; Vošvrda, Miloslav (referee)
Even though contracts for the purchase and sale of natural gas providing an offtake flexibility concerning volume and time (gas sales agreements) have been commonplace in the natural gas industry for many years, the development of techniques for pricing them has not followed at the same pace. This thesis is motivated by the changing nature of the natural gas industry in the European Union, which is asking for a mark-to-market evaluation of these contracts. The flexibility provided by these contracts is then regarded as a financial option, called a "gas swing option". Since the gas swing option is actually a set of several American puts on a spread between prices of two or more energy commodities, we devote one section of the text to the theory on spread option pricing. Due to the specific features of the energy markets the existing analytic approximations for spread option pricing are hardly applicable to our framework. That is why we employ numerical methods and model the spot price dynamics through stochastic processes capturing such features. The price of an arbitrarily chosen gas swing option is then computed in accordance with the concept of risk-neutral expectations, i.e. is considered as an expectation of discounted future cash flows for a probability structure called risk-neutral. Finally, our...
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Multifractal nature of financial markets and its relationship to market efficiency
Jeřábek, Jakub ; Vošvrda, Miloslav (advisor) ; Krištoufek, Ladislav (referee)
The thesis shows the relationship between the persistence in the financial markets returns and their efficiency. It interprets the efficient markets hypothesis and provides various time series models for the analysis of financial markets. The concept of long memory is broadly presented and two main types of methods to estimate long memory are analysed - time domain and frequency domain methods. A Monte Carlo study is used to compare the methods and selected estimators are then used on real world data - exchange rate and stock market series. There is no evidence of long memory in the returns but the stock market volatilities show clear signs of persistence.
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Modeling and Forecasting Volatility of Financial Time Series of Exchange Rates
Žižka, David ; Arltová, Markéta (advisor) ; Malá, Ivana (referee) ; Vošvrda, Miloslav (referee)
The thesis focuses on modelling and forecasting the exchange rate time series volatility. The basic approach used for the conditional variance modelling are class (G)ARCH models and their variations. Modelling of the conditional mean is based on the use of AR autoregressive models. Due to the breach of one of the basic assumption of the models (normality assumption), an important part of the work is a detailed analysis of unconditional distribution of returns enabling the selection of a suitable distributional assumption of error terms of (G)ARCH models. The use of leptokurtic distribution assumption leads to a major improvement of volatility forecasting compared to normal distribution. In regard to this fact, the often applied GED and the Student's t distributions represent the key-stones of this work. In addition, the less known distributions are applied in the work, e.g. the Johnson's SU and the normal Inverse Gaussian Distribution. To model volatility, a great number of linear and non-linear models have been tested. Linear models are represented by ARCH, GARCH, GARCH in mean, integrated GARCH, fractionally integrated GARCH and HYGARCH. In the event of the presence of the leverage effect, non-linear EGARCH, GJR-GARCH, APARCH and FIEGARCH models are applied. Using suitable models according to the selected criteria, volatility forecasts are made with different long-term and short-term forecasting horizons. Outcomes of traditional approaches using parametric models (G)ARCH are compared with semi-parametric neural networks based concepts that are widely applicable in clustering and also in time series prediction problems. In conclusion, a description is given of the coincident and different properties of the analyzed exchange rate time series. The author further summarized the models that provide the best forecasts of volatility behaviour of the selected time series, including recommendations for their modelling. Such models can be further used to measure market risk rate by the Value at Risk method or in future price estimating where future volatility is inevitable prerequisite for the interval forecasts.
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Model of EU international trade - assigning countries into subgroups in panel data
Tichý, Filip ; Hušek, Roman (advisor) ; Kodera, Jan (referee) ; Vošvrda, Miloslav (referee)
I model foreign trade among European countries by applying gravity equation model on panel data. The aim is to investigate exchange rate volatility impact on foreign trade and to test for the presence of the so-called Rose effect in relation to the Euro currency area. I develop a novel complex approach to the estimation of the gravity equation when the assumption of homogeneous reaction within the group of studied countries is relaxed. New methodology, tests and implementation is proposed. I develop several heuristic methods that permit effective clustering of countries in a selection of subgroups. The clustering process is iterative: in each step, countries are redistributed in new subgroups and the process is terminated, when no subsequent superior redistribution is possible. Finally, the effective selection of subgroups of countries is chosen to minimize an appropriately defined objective function. Results of the proposed heuristic tests suggest that no dominant method exists. Therefore, an algorithm of chaining of alternative heuristic methods is proposed. After the solution is achieved with one method, an alternative method is imposed and the search for the optimal solution continues, until the objective function reaches its minimum. The proposed methodology is applied to estimate the gravity equation of foreign trade with the extension that permits to assign countries into optimally selected subgroups using the newly introduced algorithms.
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