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Genetic programming - Java implementation
Tomaštík, Marek ; Kuba,, Martin (referee) ; Matoušek, Radomil (advisor)
This Master´s thesis implements computer program in Java, useful for automatic model generating, specially in symbolic regression problem. Thesis includes short description of genetic programming (GP) and own implementation with advanced GP operands (non-destructive operations, elitism, exptression reduction). Mathematical model is generating by symbolic regression, exacly for choosen data set. For functioning check are used test tasks. Optimal settings is found for choosen GP parameters.
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Portfólio Value at Risk a Expected Shortfall s použitím vysoko frekvenčních dat
Zváč, Marek ; Fičura, Milan (advisor) ; Janda, Karel (referee)
The main objective of this thesis is to investigate whether multivariate models using Highfrequency data provide significantly more accurate forecasts of Value at Risk and Expected Shortfall than multivariate models using only daily data. Our objective is very topical since the Basel Committee announced in 2013 that is going to change the risk measure used for calculation of capital requirement from Value at Risk to Expected Shortfall. The further improvement of accuracy of both risk measures can be also achieved by incorporation of high-frequency data that are rapidly more available due to significant technological progress. Therefore, we employed parsimonious Heterogeneous Autoregression and its asymmetric version that uses high-frequency data for the modeling of realized covariance matrix. The benchmark models are chosen well established DCC-GARCH and EWMA. The computation of Value at Risk (VaR) and Expected Shortfall (ES) is done through parametric, semi-parametric and Monte Carlo simulations. The loss distributions are represented by multivariate Gaussian, Student t, multivariate distributions simulated by Copula functions and multivariate filtered historical simulations. There are used univariate loss distributions: Generalized Pareto Distribution from EVT, empirical and standard parametric distributions. The main finding is that Heterogeneous Autoregression model using high-frequency data delivered superior or at least the same accuracy of forecasts of VaR to benchmark models based on daily data. Finally, the backtesting of ES remains still very challenging and applied Test I. and II. did not provide credible validation of the forecasts.
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Genetic programming - Java implementation
Tomaštík, Marek ; Kuba,, Martin (referee) ; Matoušek, Radomil (advisor)
This Master´s thesis implements computer program in Java, useful for automatic model generating, specially in symbolic regression problem. Thesis includes short description of genetic programming (GP) and own implementation with advanced GP operands (non-destructive operations, elitism, exptression reduction). Mathematical model is generating by symbolic regression, exacly for choosen data set. For functioning check are used test tasks. Optimal settings is found for choosen GP parameters.
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Modelování extrémních hodnot
Shykhmanter, Dmytro ; Malá, Ivana (advisor) ; Luknár, Ivan (referee)
Modeling of extreme events is a challenging statistical task. Firstly, there is always a limit number of observations and secondly therefore no experience to back test the result. One way of estimating higher quantiles is to fit one of theoretical distributions to the data and extrapolate to the tail. The shortcoming of this approach is that the estimate of the tail is based on the observations in the center of distribution. Alternative approach to this problem is based on idea to split the data into two sub-populations and model body of the distribution separately from the tail. This methodology is applied to non-life insurance losses, where extremes are particularly important for risk management. Never the less, even this approach is not a conclusive solution of heavy tail modeling. In either case, estimated 99.5% percentiles have such high standard errors, that the their reliability is very low. On the other hand this approach is theoretically valid and deserves to be considered as one of the possible methods of extreme value analysis.
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