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Variance structure of the Bitcoin currency
Pátek, Martin ; Krištoufek, Ladislav (advisor) ; Skuhrovec, Jiří (referee)
The purpose of this thesis is to explain how Bitcoin works, analyze the Bitcoin total variation and to separate the jump component of realized variance from the continuous part. In order to do so, we use estimates of quadratic variation and integrated variance. We detect jumps using a test which is based on the difference between realized variance and bipower variation. The results for BTC/USD exchange rate are then compared with the results for EUR/USD exchange rate, price of gold and for the S&P 500 index. In case of all datasets, we use data with five-minute frequency. It seems that no other work analyzing the Bitcoin total variation using the same methods to separate the jump component from the continuous part of a price process has been written so far. We found that jumps in the Bitcoin total variation are stronger than for other analyzed instruments. The results also suggest that the duration between jumps for Bitcoin considerably prolonged during the monitored period which may indicate that the behavior of price of bitcoin has stabilized over time. We also found out that the variance of price of bitcoin is higher during the monitored period in comparison with other analyzed instruments. Powered by TCPDF (www.tcpdf.org)
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Forecasting realized volatility: Do jumps in prices matter?
Lipták, Štefan ; Baruník, Jozef (advisor) ; Šopov, Boril (referee)
This thesis uses Heterogeneous Autoregressive models of Realized Volatility on five-minute data of three of the most liquid financial assets - S&P 500 Futures index, Euro FX and Light Crude NYMEX. The main contribution lies in the length of the datasets which span the time period of 25 years (13 years in case of Euro FX). Our aim is to show that decomposing realized variance into continuous and jump components improves the predicatability of RV also on extremely long high frequency datasets. The main goal is to investigate the dynamics of the HAR model parameters in time. Also, we examine whether volatilities of various assets behave differently. Results reveal that decomposing RV into its components indeed improves the modeling and forecasting of volatility on all datasets. However, we found that forecasts are best when based on short, 1-2 years, pre-forecast periods due to high dynamics of HAR model's parameters in time. This dynamics is revealed also in a year-by-year estimation on all datasets. Consequently, we consider HAR models to be inappropriate for modeling RV on such long datasets as they are not able to capture the dynamics of RV. This was indi- cated on all three datasets, thus, we conclude that volatility behaves similarly for different types of assets with similar liquidity. 1
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Applications of modern spectral tools in financial econometrics
Křehlík, Tomáš ; Baruník, Jozef (advisor) ; Hanousek, Jan (referee) ; Croux, Christopher (referee) ; Wang, Yao (referee)
Spectral tools in econometrics have lately experienced a renewed surge in interest. This dissertation contributes to this literature by providing conceptually different spectral-based methods and their applications to problems of modern economics. In the first part, we take a spectral decomposition of realized volatility and construct a multivariate GARCH style model that we fit by standard quasi-maximum likelihood and generalized autoregressive score procedures. We build our model on a belief that market agents obtain information in various time horizons and therefore form their expectations in various informational horizons. This behavior creates an overall volatility process that is a mixture of spectrum specific processes. We then apply the model to the currency markets, namely GBP, CHF, and EUR. With the help of the model confidence set test we show that the multi-scale model and the generalized autoregressive score based models produce forecasts that are in most cases superior to the competing models. Moreover, we find that most of the information for future volatility comes from the high frequency part of the spectra representing the very short investment horizons. In the second part, we provide a spectral decomposition of a system multivariate connectedness measure based on Diebold and Yilmaz...
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The Impact of High Frequency Trading on Price Volatility
Vondřička, Jakub ; Vácha, Lukáš (advisor) ; Vošvrda, Miloslav (referee)
This thesis examines an impact of high frequency trading on equity market qualities. As an indicator of market quality, stock prices realized volatility is used. To estimate the high frequency trading activity, we implement a special method of identification of high frequency orders from quote data. Study of relation between high frequency trading and market qualities is incited by growing concerns about the welfare impacts of high frequency trading and connected activities. In order to test the dependence and causality between high frequency trading activity and volatility, we implement time-scale estimation techniques. Wavelet coherence is used to study localized dependence. The analysis is amended by a robustness check, using wavelet correlation. Results show inconsistent dependence at short trading horizons and regions of significant continuous dependence at trading horizons within hours. Powered by TCPDF (www.tcpdf.org)
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Variance structure of the Bitcoin currency
Pátek, Martin ; Krištoufek, Ladislav (advisor) ; Skuhrovec, Jiří (referee)
The purpose of this thesis is to explain how Bitcoin works, analyze the Bitcoin total variation and to separate the jump component of realized variance from the continuous part. In order to do so, we use estimates of quadratic variation and integrated variance. We detect jumps using a test which is based on the difference between realized variance and bipower variation. The results for BTC/USD exchange rate are then compared with the results for EUR/USD exchange rate, price of gold and for the S&P 500 index. In case of all datasets, we use data with five-minute frequency. It seems that no other work analyzing the Bitcoin total variation using the same methods to separate the jump component from the continuous part of a price process has been written so far. We found that jumps in the Bitcoin total variation are stronger than for other analyzed instruments. The results also suggest that the duration between jumps for Bitcoin considerably prolonged during the monitored period which may indicate that the behavior of price of bitcoin has stabilized over time. We also found out that the variance of price of bitcoin is higher during the monitored period in comparison with other analyzed instruments. Powered by TCPDF (www.tcpdf.org)
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Forecasting realized volatility: Do jumps in prices matter?
Lipták, Štefan ; Baruník, Jozef (advisor) ; Šopov, Boril (referee)
This thesis uses Heterogeneous Autoregressive models of Realized Volatility on five-minute data of three of the most liquid financial assets - S&P 500 Futures index, Euro FX and Light Crude NYMEX. The main contribution lies in the length of the datasets which span the time period of 25 years (13 years in case of Euro FX). Our aim is to show that decomposing realized variance into continuous and jump components improves the predicatability of RV also on extremely long high frequency datasets. The main goal is to investigate the dynamics of the HAR model parameters in time. Also, we examine whether volatilities of various assets behave differently. Results reveal that decomposing RV into its components indeed improves the modeling and forecasting of volatility on all datasets. However, we found that forecasts are best when based on short, 1-2 years, pre-forecast periods due to high dynamics of HAR model's parameters in time. This dynamics is revealed also in a year-by-year estimation on all datasets. Consequently, we consider HAR models to be inappropriate for modeling RV on such long datasets as they are not able to capture the dynamics of RV. This was indi- cated on all three datasets, thus, we conclude that volatility behaves similarly for different types of assets with similar liquidity. 1
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Forecasting Realized Volatility Using Neural Networks
Jurkovič, Jindřich ; Baruník, Jozef (advisor) ; Krištoufek, Ladislav (referee)
In this work, neural networks are used to forecast daily Realized Volatility of the EUR/USD, GBP/USD and USD/CHF currency pairs time series. Their performan-ce is benchmarked against nowadays popular Hetero-genous Autoregressive model of Realized Volatility (HAR) and traditional ARIMA models. As a by-product of our research, we introduce a simple yet effective enhancement to HAR model, naming the new model HARD extension. Forecasting performance tests of HARD model are conducted as well, promoting it to become a reference benchmark for neural networks and ARIMA.
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Forecasting realized volatility: Do jumps in prices matter?
Lipták, Štefan ; Baruník, Jozef (advisor) ; Šopov, Boril (referee)
This thesis uses Heterogeneous Autoregressive models of Realized Volatility on five-minute data of three of the most liquid financial assets - S&P 500 Futures index, Euro FX and Light Crude NYMEX. The main contribution lies in the length of the datasets which span the time period of 25 years (13 years in case of Euro FX). Our aim is to show that decomposing realized variance into continuous and jump components improves the predicatability of RV also on extremely long high frequency datasets. The main goal is to investigate the dynamics of the HAR model parameters in time. Also, we examine if volatilities of various assets behave differently. The results reveal that decomposing RV into its components indeed im- proves the modeling and forecasting of volatility on all datasets. However, we found that forecasts are best when based on short, 1-2 years, pre-forecast periods due to high dynamics of HAR model's parameters in time. This dynamics is revealed also by a year-by-year estimation on all datasets. Con- sequently, we consider HAR models to be inapproppriate for modeling RV on such long datasets as they are not able to capture the dynamics of RV. This was indicated on all three datasets, thus, we conclude that volatility behaves similarly for different types of assets with similar liquidity. 1
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Predictive Accuracy of Competing Value-at-Risk Specifications during Crisis: An Application to CEE Financial Markets
Kroutil, Tomáš ; Baruník, Jozef (advisor) ; Seidler, Jakub (referee)
The recent worldwide Financial Crisis has increased the need for reliable financial risk measurement and management. In this thesis we evaluate and compare the accuracy of one-day-ahead out-of-sample forecasts of various Value-at-Risk models through a comprehensive assessment framework using crisis data of three CEE stock market indices (PX, WIG20 and BUX) and two benchmark stock indices (S&P 500, DAX). For building the VaR specifications we employ several GARCH extensions allowing either for asymmetry in volatility such as EGARCH, TGARCH and APARCH or long memory like FIGARCH and HYGARCH. Apart from conditional heteroscedasticity models, we also utilize realized volatility estimated by long memory ARFIMA and HAR. Individual volatility models are combined with full parametric approach, filtered historical simulation or filtered extreme value theory. This thesis shows that while VaR specifications based on logarithmic realized volatility, TGARCH and APARCH perform best overall, the benchmark - RiskMetrics model - is not significantly outperformed. The best performing model proves to be the TGARCH-t FHS, which is a combination of asymmetric and heavy-tailed GARCH filter with a historical simulation based approach. Keywords: Value-at-Risk, realized volatility, GARCH extensions, quantile modeling,...
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Methods of volatility estimation
Hrbek, Filip ; Witzany, Jiří (advisor) ; Fičura, Milan (referee)
In this masterthesis I have rewied basic approaches to volatility estimating. These approaches are based on classical and Bayesian statistics. I have applied the volatility models for the purpose of volatility forecasting of a different foreign exchange (EURUSD, GBPUSD and CZKEUR) in the different period (from a second period to a day period). I formulate the models EWMA, GARCH, EGARCH, IGARCH, GJRGARCH, jump diffuison with constant volatility and jump diffusion model with stochastic volatility. I also proposed an MCMC algorithm in order to estimate the Bayesian models. All the models we estimated as univariate models. I compared the models according to Mincer Zarnowitz regression. The most successfull model is the jump diffusion model with a stochastic volatility. On the second place they were the GJR- GARCH model and the jump diffusion model with a constant volatility. But the jump diffusion model with a constat volatilit provided much more overvalued results.The rest of the models were even worse. From the rest the IGARCH model is the best but provided undervalued results. All these findings correspond with R squared coefficient.
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