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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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Statistical properties of the liquidity and its influence on the volatility prediction
Brandejs, David ; Krištoufek, Ladislav (advisor) ; Burda, Martin (referee)
This master thesis concentrates on the influence of liquidity measures on the prediction of volatility and given the magic triangle phenomena subsequently on the expected return. Liquidity measures Amihud Illiquidity, Amivest Liquidity and Roll adjusted for high frequency data have been utilized. Dataset used for the modeling was consisting of 98 shares that were traded on S&P 100. The time range was from 1st January 2013 to 31st December 2014. We have found out that the liquidity truly enters into the return-volatility relationship and influences these variables - the magic triangle interacts. However, contrary to our hypothesis, the model shows up that lower liquidity signifies lower realized risk. This inference has been suggested by all three models (3SLS, 2SLS and OLS). Furthermore, we have used the realized variance and bi-power variation to separate the jump. Our second hypothesis that lower liquidity signifies higher frequency of jumps was confirmed only for one of two liquidity proxies (Roll) included in the resulting logit FE model. Keywords liquidity, risk, volatility, expected return, magic triangle, price jumps, realized variance, bi-power variation, three-stage least squares model, logit, high-frequency data, S&P 100 Author's e-mail david.brandejs@seznam.cz Supervisor's e-mail...
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Understanding co-jumps in financial markets
Thoma, Richard ; Baruník, Jozef (advisor) ; Vošvrda, Miloslav (referee)
This thesis focuses on impact of jumps and simultaneous jumps (co-jumps) in asset prices on future volatility. Our main contribution to the empirical literature lies in the use of panel Heterogeneous Autoregressive (HAR) model that allows us to obtain average effect of jumps for both the portfolio of 29 U.S. stocks and 8 individual market sectors our stocks belong to. On top of that we investigate the effect of sign for both jumps and co-jumps. The estimation results indicate that the impact of jumps on future volatility is positive whereas for co-jumps it is negative. We also document tendency of downward jumps and co-jumps to be followed by increase in volatility and that upward jumps and co-jumps are followed by decrease in volatility. Finally, results for individual sectors reveal that estimated effects vary across industries - for cyclical sectors volatility is in general more sensitive to negative jumps and less sensitive to positive jumps than for defensive sectors.
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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: 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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