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Multivariate Dependence Modeling Using Copulas
Klaus, Marek ; Šopov, Boril (advisor) ; Gapko, Petr (referee)
Multivariate volatility models, such as DCC MGARCH, are estimated under assumption of multivariate normal distribution of random variables, while this assumption have been rejected by empirical evidence. Therefore, the estimated conditional correlation may not explain the whole dependence structure, since under non-normality the linear correlation is only one of the dependency measures. The aim of this thesis is to employ a copula function to the DCC MGARCH model, as copulas are able to link non-normal marginal distributions to create corresponding multivariate joint distribution. The copula-based MGARCH model with uncorrelated dependent errors permits to model conditional cor- relation by DCC-MGARCH and dependence by the copula function, sepa- rately and simultaneously. In other words the model aims to explain addi- tional dependence not captured by traditional DCC MGARCH model due to assumption of normality. In the empirical analysis we apply the model on datasets consisting primarily of stocks of the PX Index and on the pair of S&P500 and NASDAQ100 in order to compare the copula-based MGARCH model to traditional DCC MGARCH in terms of capturing the dependency structure. 1
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Problémy regulace energetického sektoru jakožto přirozeného monopolu
Nováčková, Tereza ; Gapko, Petr (advisor) ; Luňáčková, Petra (referee)
UNIVERZITA KARLOVA V PRAZE FAKULTA SOCIÁLNÍCH VĚD Institut ekonomických studií Tereza Nováčková Problémy regulace energetického sektoru jakožto přirozeného monopolu Bakalářská práce Praha 2011 Abstract The thesis deals with the problems faced by the regulatory authority when monitoring natural monopolies. Three main objectives are set out within the work. Firstly, I will compare the theory of regulation with its practical application to the energy sector in the Czech Republic. The second objective covers a comparison of two methods of regulation and their impacts on a consumer and the regulated company. For this purpose prices set by regulatory authority have been compared with prices created by Price-cap method. The third objective is the analyses of electricity prices ranging from the initial operating of the regulatory authority in the Czech Republic. The outcome of the thesis is the description of the regulation of energy market in the Czech Republic focusing on the theories of regulation.
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Comparison of Value-at-Risk using various empirical methods for the portfolios of BRICT and G-7 countries in the long run
Gül, Özgür ; Baruník, Jozef (advisor) ; Gapko, Petr (referee)
This master's thesis deals with Value-at-Risk for equity portfolios. The distribution of daily returns of equity returns is not perfectly normal. Therefore, the use of the Delta- Normal Value-at-Risk (VaR) method is misleading. Accuracy of estimation may turn out to be failure for portfolios to measure VaR time to time. Therefore, two further methods, Modified VaR and Filtered Historical Simulation, are used for VaR estimation. The former estimates using Cornish-Fisher (1937) expansion and then the latter estimates using autoregressive model for mean equation, EGARCH for volatility and Filtered Historical Simulation (FHS) for VaR estimation i.e. AR (1) - EGARCH (1,1) - FHS methods; and also the performance of both the VaR estimates with Delta- Normal VaR estimate are compared. Last but not the least the implementation of various methods are discussed and analyzed on the two passive historical index portfolios, which represent some of the most attractive financial markets in the world economy.
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Value at Risk Calculation of the Czech Stock Portfolio Using Alternative Distributions
Hédl, Tomáš ; Gapko, Petr (advisor) ; Seidler, Jakub (referee)
The aim of this diploma thesis is to analyze ways of Value at Risk calculation. Its core is to get a suitable model that could most appropriately reflect the probability distribution of returns of the Czech stock portfolio that we have generated. In this thesis we find out that the returns follow unbounded distribution which was first described by Johnson (1949). Since we detect that returns are correlated we have to apply appropriate autoregressive process that removes this dependency. In the empirical part we discover an inability of models based on assumptions of normality, to correctly predict the Value at Risk. Historical simulation methods, which have promising backtesting results, are rejected because of the slow adaptation to the recent changes in the market. However, we find a way how to implement Johnson SU distribution into the GARCH model. This model, which passes all the tests, is thus able to predict Value at Risks of the portfolio most accurately. JEL Classification: C16, C22, G11 Keywords: Market risk, Value at Risk, Risk management, Johnson SU distribution
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Alternative measures of risk - application on the Central European region
Vodňanský, Ondřej ; Rippel, Milan (referee) ; Gapko, Petr (advisor)
Increasing volume of research shows that both theoretical assumptions and empirical fit of traditional mean-variance and CAPM frameworks are flawed. Hence, other risk measures are gaining popularity. Downside risk measures not only represent the theory well, they are also significant in explaining variations of stock returns. Most importantly, the definition of risk they provide is more in line with perspectives of investors. We have carried out extensive testing on a sample of companies from the Czech Republic, Germany and Poland. Our results show that Semivariance with respect to zero is the most significant risk measure while CAPM beta by itself has little use. Finally, we also analysed importance of idiosyncratic risk on CEE shares and found out that it is indeed priced on the Czech and Polish stock markets but not in Germany.
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Option pricing methods
Chrobok, Viktor ; Vlasáková Baruníková, Michaela (referee) ; Gapko, Petr (advisor)
The diploma thesis is focused on the option pricing methods. There are described basic features of the option contracts and the types of them. Then a description of 6 pricing methods is given - the Black-Scholes model, the French Black-Scholes model, the Binomial Model, the Quadratic approximation model, the Bjerksund-Stersland model and the Jump-Diffusion model. The empirical part contains an analysis of the performance of all models on the real market data. It was shown that all models except for the Jump-Diffusion one fit the data very well, yet it was impossible to determine the best one. The evidence suggests that it is better to plug a few-days-delayed implied volatility than the historical one into all of the models. It was observed that the models for pricing European options are suitable even for the American ones.
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Growth dividend from the financial markets integration in the Eurozone after the adoption of the single currency
Hassairi, Nail ; Gapko, Petr (referee) ; Dědek, Oldřich (advisor)
The introduction of the common currency in part of the European Union was a landmark event. It raised eyebrows, expectations and gloomy forecasts. Optimists saw the currency bringing about efficiencies in variety of different ways and industries. This thesis is preoccupied with financial markets. The thesis of this work is that Euro triggered integration on financial markets in countries that joined the project of common currency. The work is trying to gauge this ongoing financial integration and find a measure that would represent it. After finding this measure it is a goal of this paper to estimate if the ongoing financial integration contributed to higher growth prospects in the economies involved.
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Weather risk in the natural gas market
Vyležík, Tomáš ; Janda, Karel (advisor) ; Gapko, Petr (referee)
This thesis deals with the impact of weather on the natural gas market. We describe the development of the natural gas market in the recent past and its current structure. Both these contingencies contributed to the growing importance of hedging against weather risk. Weather is unambiguously the primary determinant of demand in the natural gas market. For that reason, we build a model predicting consumption in the Czech natural gas market with respect to its temperature sensitivity. Such an analysis frequently serves as the first indicator of the need for weather risk hedging, which is since the 90's commonly done with weather derivatives. Therefore we go through so called burn analysis that determines the fair price of an option with regard to past temperature measurements.
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Dynamic Model of Losses of Creditor with a Large Mortgage Portfolio
Šmíd, Martin ; Gapko, Petr
We propose a dynamic model of mortgage credit losses. We assume borrowers to hold assets covering the instalments and to own a real estate which serves as a collateral; both the value of the assets and the price of the estate follow general stochastic processes driven by common and individual factors. We describe the correspondence between the common factors, the percentage of defaults and the loss given default and we suggest a procedure of econometric estimation of the model.
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Modeling a distribution of mortgage credit losses
Gapko, Petr ; Šmíd, Martin
One of the biggest risks arising from financial operations is the risk of counterparty default, commonly known as a “credit risk”. Leaving unmanaged, the credit risk would, with a high probability, result in a crash of a bank. In our paper, we will focus on the credit risk quantification methodology. We will demonstrate that the current regulatory standards for credit risk management are at least not perfect, despite the fact that the regulatory framework for credit risk measurement is more developed than systems for measuring other risks, e.g. market risks or operational risk. Generalizing the well known KMV model, standing behind Basel II, we build a model of a loan portfolio involving a dynamics of the common factor, influencing the borrowers’ assets, which we allow to be non-normal. We show how the parameters of our model may be estimated by means of past mortgage deliquency rates.
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