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Quantitative Methods of Risk Control
Marcinek, Daniel ; Hurt, Jan (advisor) ; Hendrych, Radek (referee)
This thesis deals with stock modelling using ARCH and GARCH time series. Important aspect of stock modelling is to capture volatility correctly. Volatility in finance is usually defined as a standard deviation of asset returns. Many different models, which are summarized in the first part of this thesis, are used to model volatility. This thesis focus on multivariate volatility models including multivariate GARCH models. An approach to constructing a conditional maximum likelihood estimate to these methods is given. Discussed theory is applied on real financial data. In numeric application there is a construction of a volatility estimates for two specific stocks using models described in the first part of this thesis. Using the same financial data various bivariate models are compared. Based on comparison using maximum likelihood a specific model for these stocks is recommended. Powered by TCPDF (www.tcpdf.org)
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Multivariate GARCH
Maďar, Milan ; Hurt, Jan (advisor) ; Branda, Martin (referee) ; Mazurová, Lucie (referee)
4 Title: Multivariate GARCH Author: Mgr. Milan Mad'ar Department: Katedra pravděpodobnosti a matematické statistiky Abstract: This thesis will examine the regional and global linkages as evi- dence of integration of stock markets in Frankfurt, Amsterdam, Prague and the U.S. Therefore we will utilize the multivariate GARCH approach that investigates the dynamics of volatility transmission of related foreign exchange rates. Also, we will define three basic model classes. For each of the model classes a theoret- ical review, basic properties and estimation procedure with proofs are provided. We illustrate each approach by applying the models to daily market data. The two main aims of the thesis are to discuss and report the existence of regional and global stock markets linkages and provide a comparison of such multivariate GARCH models on the data sample. The main contribution of the thesis is that it treats the data in the context of real development in financial markets and takes into account the real situation during and after the financial crisis of 2008. We find out that the estimated time-varying conditional correlations indicate limited integration among the markets, which implies that investors can benefit from the risk reduction by investing in the different stock markets, especially during the crisis....
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Multivariate Financial Time Series
Veselý, Daniel ; Cipra, Tomáš (advisor) ; Kopa, Miloš (referee)
In this work we will describe methods for modeling multivariate financial time series. We will concentrate on both modeling expected value by multi- variate Box-Jenkins processes and primarily on modeling conditional corre- lations and volatility. Our main object will be DCC (Dynamic Conditional Correlation) model, estimation of its parameters and some other general- izations. Then we will programme DCC model in statistical software R and apply on real data. In applications we will concentrate on problem of high dimension of financial time series and on modeling conditional correlations data with outliers.
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Multivariate GARCH
Maďar, Milan ; Branda, Martin (referee) ; Mazurová, Lucie (referee)
4 Title: Multivariate GARCH Author: Mgr. Milan Mad'ar Department: Katedra pravděpodobnosti a matematické statistiky Abstract: This thesis will examine the regional and global linkages as evi- dence the integrated markets consist of stock markets in Frankfurt, Amsterdam, Prague the U.S. Therefore we will utilize the multivariate GARCH approach that investigates into the dynamics of volatility transmission of related foreign exchange rates. Also, we will define three basic model classes. For each of the model classes a theoretical review, basic properties and estimation procedure with proofs are provided. We illustrate approach by applying the models to daily market data. Our two main aims are discussing and reporting the existence of regional and global stock markets linkages and provide a comparison of such mul- tivariate GARCH models on the data sample. We find out that the estimated time-varying conditional correlations indicate limited integration among the mar- kets which implies that investors can benefit from the risk reduction by investing in the different stock markets especially during the crisis. Keywords: multivariate GARCH, VECH, BEKK, O-GARCH, GO-GARCH, CCC, DCC
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Multivariate generalized autoregressive conditional heteroscedasticity models
Nováková, Martina ; Pešta, Michal (advisor) ; Maciak, Matúš (referee)
This master thesis deals with extension of the univariate GARCH model to multivari- ate models. We present individual models and deal with methods of their estimation. Then we describe some statistical tests for diagnosting the models. We have programmed in the statistical software R one of them - the Ling-Li test. Afterwards we apply selected models to real data of stock market index S&P 500, stock market index Russell 2000 and stocks of crude oil. For the GO-GARCH model, we compare all available estimation methods and show their differences. Then we compare the results of all models with each other and also with univariate models in terms of estimates of conditional variances, estimates of conditional correlations and also in terms of computational complexity. 1
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Quantitative Methods of Risk Control
Marcinek, Daniel ; Hurt, Jan (advisor) ; Hendrych, Radek (referee)
This thesis deals with stock modelling using ARCH and GARCH time series. Important aspect of stock modelling is to capture volatility correctly. Volatility in finance is usually defined as a standard deviation of asset returns. Many different models, which are summarized in the first part of this thesis, are used to model volatility. This thesis focus on multivariate volatility models including multivariate GARCH models. An approach to constructing a conditional maximum likelihood estimate to these methods is given. Discussed theory is applied on real financial data. In numeric application there is a construction of a volatility estimates for two specific stocks using models described in the first part of this thesis. Using the same financial data various bivariate models are compared. Based on comparison using maximum likelihood a specific model for these stocks is recommended. Powered by TCPDF (www.tcpdf.org)
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Multivariate GARCH
Maďar, Milan ; Branda, Martin (referee) ; Mazurová, Lucie (referee)
4 Title: Multivariate GARCH Author: Mgr. Milan Mad'ar Department: Katedra pravděpodobnosti a matematické statistiky Abstract: This thesis will examine the regional and global linkages as evi- dence the integrated markets consist of stock markets in Frankfurt, Amsterdam, Prague the U.S. Therefore we will utilize the multivariate GARCH approach that investigates into the dynamics of volatility transmission of related foreign exchange rates. Also, we will define three basic model classes. For each of the model classes a theoretical review, basic properties and estimation procedure with proofs are provided. We illustrate approach by applying the models to daily market data. Our two main aims are discussing and reporting the existence of regional and global stock markets linkages and provide a comparison of such mul- tivariate GARCH models on the data sample. We find out that the estimated time-varying conditional correlations indicate limited integration among the mar- kets which implies that investors can benefit from the risk reduction by investing in the different stock markets especially during the crisis. Keywords: multivariate GARCH, VECH, BEKK, O-GARCH, GO-GARCH, CCC, DCC
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Multivariate Financial Time Series
Veselý, Daniel ; Cipra, Tomáš (advisor) ; Kopa, Miloš (referee)
In this work we will describe methods for modeling multivariate financial time series. We will concentrate on both modeling expected value by multi- variate Box-Jenkins processes and primarily on modeling conditional corre- lations and volatility. Our main object will be DCC (Dynamic Conditional Correlation) model, estimation of its parameters and some other general- izations. Then we will programme DCC model in statistical software R and apply on real data. In applications we will concentrate on problem of high dimension of financial time series and on modeling conditional correlations data with outliers.
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Modelování ve finanční analýze
Maďar, Milan ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
In this thesis we study the regional and global linkages as evidence of markets integration of the stock markets in Frankfurt, Amsterdam, Prague the U.S. and the dynamics of volatility transmission of related foreign exchange rates using multivariate GARCH approach. For each of the model classes, a theoretical review, basic properties and estimation procedure are provided. We illustrate approach by applying the models to daily market data. Our two main aims are discussing and report the existence of regional and global stock markets linkages and provide comparison of such multivariate GARCH models on the data sample. We find out that the estimated time-varying conditional correlations indicate limited integration among the markets which implies that investors can benefit from the risk reduction by investigating in the different stock markets especially during the crisis.
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Multivariate GARCH
Maďar, Milan ; Hurt, Jan (advisor) ; Branda, Martin (referee) ; Mazurová, Lucie (referee)
4 Title: Multivariate GARCH Author: Mgr. Milan Mad'ar Department: Katedra pravděpodobnosti a matematické statistiky Abstract: This thesis will examine the regional and global linkages as evi- dence of integration of stock markets in Frankfurt, Amsterdam, Prague and the U.S. Therefore we will utilize the multivariate GARCH approach that investigates the dynamics of volatility transmission of related foreign exchange rates. Also, we will define three basic model classes. For each of the model classes a theoret- ical review, basic properties and estimation procedure with proofs are provided. We illustrate each approach by applying the models to daily market data. The two main aims of the thesis are to discuss and report the existence of regional and global stock markets linkages and provide a comparison of such multivariate GARCH models on the data sample. The main contribution of the thesis is that it treats the data in the context of real development in financial markets and takes into account the real situation during and after the financial crisis of 2008. We find out that the estimated time-varying conditional correlations indicate limited integration among the markets, which implies that investors can benefit from the risk reduction by investing in the different stock markets, especially during the crisis....
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