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Asymmetric volatility modelling in finance
Ploužková, Karolína ; Zichová, Jitka (advisor) ; Vejmělka, Petr (referee)
This bachelor thesis deals with modelling volatility in finance. The aim of the thesis is to introduce the models that can be used to this purpose. We focus on the GARCH and EGARCH models. For both models, we present their definition and investigate stationarity, the existence of unconditional moments and the correlation structure. We also present the GED distribution that is used in volatility modelling. In the practi- cal part of the thesis, we show process simulations for different choices of parameters, investigate the accuracy of the parameter estimates, and finally perform an application of the GARCH and EGARCH models to the logarithmic returns of the Apple stocks. 1
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Bonus hunger in motor insurance
Povolná, Eliška ; Mazurová, Lucie (advisor) ; Vejmělka, Petr (referee)
The thesis deals with the analysis of bonus-malus systems used in motor insurance to adjust the amount of the premium depending on the number of claims reported by the driver. It focuses on the mathematical description of a phenomenon called bonus hunger, where a driver prefers not to claim a claim in order not to be placed in a bonus class with a higher premium for the following period. The thesis describes the procedure for choosing the optimal retention using Lemaire's algorithm on the chosen model. In the practical part, the algorithm is implemented in software and values are calculated for a system based on the conditions of one Czech insurance company. 1
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Recursive estimates of financial time series
Vejmělka, Petr ; Cipra, Tomáš (advisor)
This work aims to describe the method of recursive estimation of time series with conditional volatility, used mainly in finance. First, there are described the basic types of models with conditional heteroskedasticity (GARCH) and princi- ples of state-space modeling demonstrated by means of linear models AR and ARMA. Subsequently, there are derived algorithms for recursive estimation of parameters of the GARCH model and its possible modifications including the ones for which recursive estimation formulas have not been yet derived in lit- erature. These algorithms are tested in a simulation study, where their appli- cability in practice is investigated. Finally, we apply these algorithms to real high-frequency data from the stock exchange. The practical part is done us- ing the software Mathematica 11.3. The work also serves as an overview of the current state of online modeling of financial time series. 1
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Recursive estimates of financial time series
Vejmělka, Petr ; Cipra, Tomáš (advisor)
This work aims to describe the method of recursive estimation of time series with conditional volatility, used mainly in finance. First, there are described the basic types of models with conditional heteroskedasticity (GARCH) and princi- ples of state-space modeling demonstrated by means of linear models AR and ARMA. Subsequently, there are derived algorithms for recursive estimation of parameters of the GARCH model and its possible modifications including the ones for which recursive estimation formulas have not been yet derived in lit- erature. These algorithms are tested in a simulation study, where their appli- cability in practice is investigated. Finally, we apply these algorithms to real high-frequency data from the stock exchange. The practical part is done us- ing the software Mathematica 11.3. The work also serves as an overview of the current state of online modeling of financial time series. 1
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Recursive estimates of financial time series
Vejmělka, Petr ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This work aims to describe the method of recursive estimation of time series with conditional volatility, used mainly in finance. First, there are described the basic types of models with conditional heteroskedasticity (GARCH) and princi- ples of state-space modeling demonstrated by means of linear models AR and ARMA. Subsequently, there are derived algorithms for recursive estimation of parameters of the GARCH model and its possible modifications including the ones for which recursive estimation formulas have not been yet derived in lit- erature. These algorithms are tested in a simulation study, where their appli- cability in practice is investigated. Finally, we apply these algorithms to real high-frequency data from the stock exchange. The practical part is done us- ing the software Mathematica 11.3. The work also serves as an overview of the current state of online modeling of financial time series. 1
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Multivariate models of volatility
Vejmělka, Petr ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
In this work, we deal with the modeling of multivariate financial time series. First, linear models of multivariate time series are described and further special features of the financial time series. In the next part of the thesis, we focus on modeling multivariate volatility and present several models that can be used in this context. In the practical part of the work, we apply some of these models on real data using the software systems EViews 9 and RATS 8. As the first one, we analyze gradually two-dimensional and five-dimensional financial time series. The aim of thesis is to survey the temporary state of multivariate volatility modeling in financial time series including practical experience with specialized software. 1
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