|
|
Dynamic Asset Pricing Models
Tabiš, Peter ; Witzany, Jiří (advisor) ; Stádník, Bohumil (referee)
Field of examination is theoretical and empirical review of dynamic CAPM models that assume non constant volatility and correlation. In other words time evolution is considered in estimation process. As theoretical basement is recommended to be R. Engle's (Dynamic Conditional Beta) research and other sources.
|
|
|
GARCH models and R
Jánoš, Andrej ; Bašta, Milan (advisor) ; Hejdová, Martina (referee)
The work is devoted to the concept of volatility and the basic models of volatility ARCH and GARCH. Firstly, volatility, properties of volatility, general structure of the models and historical volatility is described. Then the ARCH and GARCH volatility models are introduced and their properties, estimation methods and the possibility of implementation of these models in modeling and forecasting volatility are discussed. A substantial part of this work is a detailed application of the described models to some particular time series (both simulated and real) using the R program. We analyze the real data capturing the evolution of Prague stock index PX. The key aspect of the work is to provide enough theoretical knowledge and practical skills for a reader to fully understand the mentioned models and to be able to apply them in practise.
|
|
| |
|
|
Mathematical modelling of crown rate
UHLÍŘOVÁ, Žaneta
This thesis is focused on mathematical modelling of exchange rate CZK/USD in 1991 - 2014. Time series was divided into 5 parts. First Box-Jenkins methodology models were examined, especially ARIMA model. Unfortunately, the model could not be used because none of the time series showed correlation. The time series is considered as a white noise. The data appear to be completely random and unpredictable. The time series have not constant variance neither normal distribution and therefore GARCH volatility model was used as the second model. It is better not to divide time series when using model of volatility. Volatility model contributes to more accurate prediction than the standard deviation. Results were calculated in RStudio software and MS Excel.
|
|
|
Mathematical modeling of gold price
ŠMARDA, Tomáš
This bachelor thesis is focused on mathematical modelling of gold price. After introducing basic models of Box-Jenkins methodology and models of conditional hetoskedasticity, the time series was modelled by random walk process. The time series has not constant variance, neither normal distribution, therefore for the second model was considered volatility model GARCH. Using the volatility model GARCH is possible to refine prediction intervals for forecast one step ahead. Results were calculated in R software and MS Excel.
|
|
| |
|
|
Volatility Modeling of the PX Index
Dvořáčková, Anna ; Borovička, Adam (advisor) ; Zouhar, Jan (referee)
This thesis is focused on modeling of the real financial time series of the PX Index using linear and nonlinear volatility models. In the theoretical part the major terms and typical properties of the financial time series are presented and it is followed by the theoretical description of the linear and nonlinear volatility models including a general volatility model building. The key part of this thesis is the practical application of chosen linear and nonlinear volatility models on the time series of log returns of the PX Index. By using the real data set we verify if the volatility models are really capable of explaining the theoretical properties of the financial time series, such as volatility clustering, leptokurtic distribution and leverage effect.
|
|
|
Models of inflation and its volatility in CZ
Bisová, Sára ; Hušek, Roman (advisor) ; Pelikán, Jan (referee)
This paper focuses on analysing and modelling inflation and its dynamics in Czech Republic applying a special kind of econometric models. Firstly economic theory of inflation is mentioned - fundamental terms, measuring methods of inflation, the way Czech national bank is monitoring the inflation and obviously a short summary of historical evolution of inflation in Czech economy. In the second part of this paper two econometric concepts of modelling time series are introduced - vector autoregression models (VAR models) and volatility models, concretely ARCH and GARCH models. In connection with the VAR models, Granger causality, impulse response functions, cointegration and error correction models are described. The empirical part includes application of selected models on real time series of chosen macroeconomic indicators. The estimation outputs are interpreted and forecasts are implemented. The quality of chosen econometric models for modelling inflation in Czech Republic is discussed.
|
|
|
Structure and properties of GARCH(1,1) model
Maštalíř, Jakub ; Pígl, Jan (advisor)
The aim of this thesis is to introduce the reader an econometric approach to financial time series volatility modeling and scrutinize construction, properties and constraints of the popular GARCH(1,1) model when applying it on real market data and in wider sense than it's usually presented in reference literature. In the section 1 we'll repeat some important statistical terms of time series econometrics, which will be needed in next sections. We'll talk a little bit more generally about volatility of an asset, its modeling and measuring at all, because the true values are actually unknown and we observe just its demonstration on the markets. We'll mention some important statistical tools operating as an irreplaceable component of the GARCH(1,1) model, which will be introduce in the section 2. We'll scrutinize its specific properties, advantages, constraints and indeed the statistical inference. Because it's considered as a flexible model with rather general structure we'll also discuss some complications which can occur during its applications and convenient ways to solve them. Implementation of the model will be presented in the section 3. We'll use real market data and show clear demonstration of the scrutinized properties. At the end we'll verify how the model is significant when explaining the volatility of an asset.
|
|
|
Macroeconomic Modeling of the Economy of CR during the Accession to the EU
Švarcová, Radka ; Hušek, Roman (advisor) ; Štěpán, Josef (referee) ; Nováček, Jan (referee)
Práce zkoumá možnosti analýzy mechanismů působících během vstupu ČR do EU pomocí 2 ekonometrických modelů. První model je makroekonomický, vychází z Romerova IS-MP modelu. Je specifikovaný a odhadnutý jako GARCH model za použití časových řad pozorování, na jeho základě jsou stanoveny předpovědi. Výsledky ukazují velkou propojenost ekonomiky ČR s ekonomikou EU v období před vstupem do EU. Druhý model je mikroekonomický, tzv. "model obecné rovnováhy" (GE model). Jeho parametry jsou kalibrovány na základě dat z jednoho období. Model lze využít k simulacím změn souvisejících se vstupem ČR do EU.
|
guest ::
