|
| |
|
|
Multivariate ARCH and GARCH models
Šafránková, Jana ; Prášková, Zuzana (advisor) ; Hurt, Jan (referee)
We study multivariate ARCH and GARCH models and their subsequent application to simulated and real data. In discussed models the conditional variance matrix is considered to be a function of lagged data process which is the subject of study. In case of GARCH models the conditional variance matrix is dependent on own lagged values, too. First of all, we deal with univariate ARCH and GARCH models to get some theoretical basis. The subsequent study extends this basis to multivariate models. A survey of multivariate GARCH models is presented in the next part of this thesis. Further study is devoted to maximum likelihood estimators of these models and we deal with alternatives to multivariate normal distribution which is a standard assumption of this method. We occupy ourselves with tests of these models, too. We mention both preestimation tests and postestimation tests to verify the adequacy of models. In conclusion we give practical examples which show di±culties of applications of these models for real data.
|
|
| |
|
|
Credit Scoring Models Based on Monitoring the Behaviour of Debtors
Škovroňová, Lenka ; Marosi, Gabriel (advisor) ; Hurt, Jan (referee)
Text of this thesis is divided into five main parts. In opening part we put mind to credit risk and credit process, describing various bank clients. There are trends in loans development by client sectors underlined. In second part there is a survey of mathematical models which are widely used in real life for client creditworthiness analysis. In next part you can find a detailed description of theory for logistic regression model and for new developed random walk model resulting from commercial KMV model. Suitting of random walk model to predicting default of retail clients on their overdrafts is mentioned. The fourth part begins with description of data used. Then the numeric work for both mentioned models is focused, using results of logistic regression model as performance measure of new random walk model. The conclusion pays to draw out some possible future improvements of new model.
|
|
| |
|
| |
|
|
Contemporary measures of financial risk
Leder, Ondřej ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The main goal of this work is to talk about some financial risks and to introduce some methods of measuring them. The most important part of this work is the value at risk, its extension in form of conditional value at risk and introduction of some of its possible alternatives, which are expectile and spectral risk measures. For this it is needed to give a theoretical framework from the theory of probability. Its goal is to show the similarity of expectile and quantile, because value at risk is practicaly a quantile. Another goal of this fork is to show some weak properties of VaR and to practically illustrate the possibility of using expectile as an alternative to VaR. Powered by TCPDF (www.tcpdf.org)
|
|
| |
|
| |
|
|
Optimization methods in finance
Baník, Peter ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
In this diploma paper we discuss selected optimization methods and mathematical programming models. We focus on optimization models of optimal portfolio selection problem. We consider the problem of finding optimal portfolio under criterion of maximizing expected return and risk minimizing. For selected risk measures we use convenient mathematical models. There are adequate optimization techniques for problems of linear and quadratic programming. For general nonlinear problems we use advanced stochastic optimization algorithms. We numerically illustrate the methods on real data examples using the Mathematica software. Presented results give comparisons both for models and methods. We also focus on computational complexity of optimization algorithms and study the influence of input parameters on the results.
|
guest ::
