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Stochastic Catastrophe Model Cusp
Voříšek, Jan ; Vošvrda, Miloslav (advisor)
Title: Stochastic Catastrophe Model Cusp Author: Jan Voříšek Department: Department of Probability and Mathematical Statistics Supervisor: Prof. Ing. Miloslav Vošvrda, CSc., Czech Academy of Sciences, Institute of Information Theory and Automation Abstract: The goal of this thesis is to analyze the stochastic cusp model. This task is divided into two main topics. The first of them concentrates on the stationary density of the cusp model and statistical testing of its bimodality, where power and size of the proposed tests are simulated and compared with the dip test of unimodality. The second main topic deals with the transition density of the stochastic cusp model. Comparison of approximate maximum likelihood approach with traditional finite difference and numerical simulations indicates its advantage in terms of speed of estimation. An approximate Fisher information matrix of general stochastic process is derived. An application of the cusp model to the exchange rate with time-varying parameters is estimated, the extension of the cusp model into stochastic bimodality model is proposed, and the measure of probability of intrinsic crash of the cusp model is suggested. Keywords: stochastic cusp model, bimodality testing, transition density ap- proximation
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Measuring credit risk for portfolios with heavy-tailed risk factors
Jablonský, Petr ; Vošvrda, Miloslav (advisor) ; Janda, Karel (referee)
Measuring and managing credit risk constitute one of the most important processes within bank risk management. Classical credit risk models assume multivariate normality for distribution of underlying risk factors. Resulting methods offer analytical simplicity and computational efficiency but disregard of extreme joint events since their probability is too small. Recently several studies have doubted multivariate normality assumption saying that if we accept this assumption we might seriously underestimate downside risk of given credit portfolio. The master thesis provides with an insight into the problem of modelling credit risk under assumption of heavy tailed risk factors. We first present necessary mathematical preliminaries of copula functions which stand for an alternative method of modelling multivariate dependence structures. Next we introduce a credit risk model for bond portfolio with heavy tailed risk factors. At last we carry out several simulations on portfolios of different riskiness and compare to what extent the results from both mentioned models differ.
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Interest rate derivatives offered by Czech banks : types, usage and pricing
Nevrkla, Ladislav ; Dědek, Oldřich (advisor) ; Vošvrda, Miloslav (referee)
This rigorous thesis describes interest rate derivatives in context of Czech banks. The interest rate derivative is defined for the purpose of this thesis as a financial instrument where the interest rate instrument is its underlying asset, which is denominated in a single currency and its payoff is dependent on future interest rate development. First part deals with an analysis of the bank sector and the identified products are described. Range of the offered products serves as an indicator of the interest rate derivative market development. Second part analyzes pricing models and tries to answer a question whether the banks price the derivatives products at fair value. The yield curve construction is described and Black - Scholes and Hull - White models follow. The whole structure of this thesis aims to cover the detailed description of the interest rate derivatives. Powered by TCPDF (www.tcpdf.org)
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Fractality of Stock Markets: A Comparative Study
Krištoufek, Ladislav ; Baruník, Jozef (advisor) ; Vošvrda, Miloslav (referee)
The main focus of the thesis is the introduction of new method for interpretation of fractality aspects of financial time series together with its application. We begin with description of various techniques of estimation of Hurst exponent - rescaled range, modified rescaled range and detrended fluctuation analysis. Further on, we present original theoretical results based on simulations of three mentioned procedures which have not been presented in literature yet. The results are then used in the new method of time-dependent Hurst exponent with confidence intervals developed in this thesis. Moreover, we show important advantage of using the mentioned techniques together to clearly distinguish between independent, trending, short-term dependent and long-term dependent properties of the time series. We eventually apply the proposed procedure on 13 different world stock indices and come to interesting results. To the author's best knowledge, the thesis presents the broadest application of timedependent Hurst exponent on stock indices yet.
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Discrete Dynamic Endogenous Growth Model: Derivation, Calibration and Simulation
Kodera, J. ; Van Tran, Q. ; Vošvrda, Miloslav
Endogenous economic growth model were developed to improve traditional growth models with exogenous technological changes. There are several approaches how to incorporate technological progress into a growth model. Romer was the first author who has introduced it by expanding the variety of intermediate goods. Overall, the growth models are often continuous. In our paper we formulate a discrete version of Romer's model with endogenous technological change based on expanding variety of intermediates, both in the final good sector and in the research-development sector, where the target is to maximize present value of the returns from discovering of intermediate goods which should prevail introducing costs. These discrete version then will be calibrated by a numerical example. Our aim is to find the solution and analyse the development of economic variables with respect to external changes.
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Capital market efficiency in the Ising model environment: Local and global effects
Krištoufek, Ladislav ; Vošvrda, Miloslav
Financial Ising model is one of the simplest agent-based models (building on a parallel between capital markets and the Ising model of ferromag- netism) mimicking the most important stylized facts of financial returns such as no serial correlation, fat tails, volatility clustering and volatility persistence on the verge of non-stationarity. We present results of Monte Carlo simulation study investigating the relationship between parameters of the model (related to herding and minority game behaviors) and crucial characteristics of capital market e ciency (with respect to the e cient market hypothesis). We find a strongly non-linear relationship between these which opens possibilities for further research. Specifically, the existence of both herding and minority game behavior of market participants are necessary for attaining the e cient market in the sense of the e cient market hypothesis.
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Trading strategies based on estimates of conditional distribution of stock returns
Sedlačík, Adam ; Baruník, Jozef (advisor) ; Vošvrda, Miloslav (referee)
In this thesis, a new trading strategy is proposed. By the help of quantile regression, the conditional distribution functions of stock market returns are estimated. Based on the knowledge of the distribution the strategy produced buying and selling signals which together with a weight function derived from exponential moving averages determines how much and when to buy or sell. The strategy performs better than the market in terms of absolute return and the Sharpe ratio in-sample, but it does not provide satisfactory results out-of-sample.
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Stochastic Catastrophe Model Cusp
Voříšek, Jan ; Vošvrda, Miloslav (advisor)
Title: Stochastic Catastrophe Model Cusp Author: Jan Voříšek Department: Department of Probability and Mathematical Statistics Supervisor: Prof. Ing. Miloslav Vošvrda, CSc., Czech Academy of Sciences, Institute of Information Theory and Automation Abstract: The goal of this thesis is to analyze the stochastic cusp model. This task is divided into two main topics. The first of them concentrates on the stationary density of the cusp model and statistical testing of its bimodality, where power and size of the proposed tests are simulated and compared with the dip test of unimodality. The second main topic deals with the transition density of the stochastic cusp model. Comparison of approximate maximum likelihood approach with traditional finite difference and numerical simulations indicates its advantage in terms of speed of estimation. An approximate Fisher information matrix of general stochastic process is derived. An application of the cusp model to the exchange rate with time-varying parameters is estimated, the extension of the cusp model into stochastic bimodality model is proposed, and the measure of probability of intrinsic crash of the cusp model is suggested. Keywords: stochastic cusp model, bimodality testing, transition density ap- proximation
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