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Estimation and Application of the Tail Index
Pokorná, Markéta ; Šopov, Boril (advisor) ; Zelený, Tomáš (referee)
Examining the nature of extreme values plays an important role in financial risk management. This thesis investigates tail behaviour of distribution of re- turns using the framework of univariate Extreme Value Theory. The empirical research was conducted on the S&P 500 index and its seven constituents. The goal of this thesis was to use the Hill method to estimate the tail index of the series which characterizes the tail behaviour, especially the speed of the tail decay. To select the tail threshold several graphical methods were performed as they represent empirical measures of model stability. Classical Hill plots as well as alternative Hill plots and smoothing procedure were presented. The threshold choice based on stable regions in the graphs was found to be highly subjective. Hill method modified by Huisman was used instead and the results confirmed that the classical Hill method yields estimates which overestimate the tail thickness. All the examined series were found to have heavy tails with polynomial tail decay. This thesis stressed the need to model the left and the right tail separately as both extreme losses and profits are important depending on whether an investor takes a long or a short position on portfolio. Finally, the tail index was used to demonstrate the need to compute the...
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Stability of the Financial System: Systemic Dependencies between Bank and Insurance Sectors
Procházková, Jana ; Šopov, Boril (advisor) ; Janda, Karel (referee)
The central issue of this thesis is investigating the eventuality of systemic break- downs in the international financial system through examining systemic depen- dence between bank and insurance sectors. Standard models of systemic risk often use correlation of stock returns to evaluate the magnitude of intercon- nectedness between financial institutions. One of the main drawbacks of this approach is that it is oriented towards observations occurring along the central part of the distribution and it does not capture the dependence structure of outlying observations. To account for that, we use methodology which builds on the Extreme Value Theory and is solely focused on capturing dependence in extremes. The analysis is performed using the data on stock prices of the EU largest banks and insurance companies. We study dependencies in the pre- crisis and post-crisis period. The objective is to discover which sector poses a higher systemic threat to the international financial stability. Also, we try to find empirical evidence about an increase in interconnections in recent post- crisis years. We find that in both examined periods systemic dependence in the banking sector is higher than in the insurance sector. Our results also in- dicate that extremal interconnections in the respective sectors increased,...
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Trading Volume and Volatility in the US Stock Markets
Juchelka, Tomáš ; Šopov, Boril (advisor) ; Džmuráňová, Hana (referee)
This thesis investigates the relationship between trading volume and stock re- turn volatility using GARCH model in the framework of Mixture of Distri- bution Hypothesis. Analysis is carried out for five well-known stocks selected from the American S&P500 stock index. Our approach was to extend the vari- ance equation of the well known GARCH model on the trading volume which was split into three explanatory variables capturing different effects of volume on volatility. Apart from the relationship itself, we examined the changes of GARCH and ARCH parameters after the inclusion of volume, implicitly testing the Mixture of Distribution Hypothesis. Interesting results and implications for future research were identified. Firstly, we highlight the appropriateness of the volume decomposition into expected and unexpected volume, where all the vol- ume parameters turned out to be statistically significant. General observation was that the increase of both expected and unexpected trading volume leads to the increase of volatility. On the other hand, negative volume shocks tend to decrease it. Eventhough we performed the analysis with lagged and also contemporaneous volume, we were not able to confirm that the inclusion of volume leads to insignificance of the ARCH and GARCH parameters, thus not confirming the...
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The Nelson-Siegel Model: Present Application and Alternative Lambda Determination
Marek, Jan ; Šopov, Boril (advisor) ; Avdulaj, Krenar (referee)
This thesis contributes to the topic of yield curve modelling by revaluing the famous Nelson-Siegel model in the relatively outdated but very parsimonious version. In order to make this framework applicable to present yield curves of government bonds, we introduce an alternative model dealing with an appropri- ateness of the possibly overlooked model parameter lambda. By incorporating the sound methodology, we model the yield curves of the three currency regions - EUR, USD and GBP - and assess both in-sample fit and forecasting perfor- mance. Whereas the in-sample predicting generally achieves the best results with the alternative model predicting model coefficients, especially for longer maturities, the out-of-sample forecasting seems more complicated. Actually, the detail analysis show an interesting connection between efficiencies of the models and bond market volatilities. On the base of our research, the model directly extrapolating yields appears to be more suitable for more volatile markets. JEL Classification C51, C53, C61, G17 Keywords Yield Curve, Nelson-Siegel, Newton Optimi- zation Method Author's e-mail honzamarek92@gmail.com Supervisor's e-mail boril.sopov@gmail.com
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Procyclicality of Bank Lending and Provisioning Behavior
Svoboda, Jan ; Šopov, Boril (advisor) ; Lešanovská, Jitka (referee)
The aim of this paper is to investigate the procyclical behavior of banks in terms of lending and loan loss provisioning, and its dynamics with regard to the adoption of the Basel II capital regulation. Using bank-level and country-level panel data spanning from 1996 to 2013 we answer this question for the OECD and BRIC countries. We find a positive effect of bank capitalization on loans growth, which, perhaps due to the recent financial crisis, weakened after 2008. Together with evidence of income smoothing and capital management we also find strong cyclical behavior of banks in terms of loan loss provisioning. At the same time, we do not find any robust changes to this behavior after the introduction of the Basel II capital regulation. We fill a gap in the empirical literature as there has been hardly any research done on changes brought forward by the adoption of the Basel II capital regulation. The results may be therefore of interest for regulators and other professionals. Moreover, we use in our analysis data for BRIC countries, which have been often neglected.
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Volatility Spillovers and Response Asymmetry: Empirical Evidence from the CEE Stock Markets
Dovhunová, Veronika ; Baruník, Jozef (advisor) ; Šopov, Boril (referee)
In this thesis, we examine the volatility spillovers and its response asymmetry due to neg- ative or positive shocks with the use of volatility spillover indices proposed by Baruník et al. (2013). This novel methodology extends the original spillover index framework introduced by Diebold & Yilmaz (2009) by utilizing the non-parametric measures of volatility based on the high frequency data, the realized variance and realized semivariances. Our analysis is performed on two datasets, the first one covering the selected Central and Eastern European stock market indices of the Czech Republic, Hungary and Poland, and the second one extending the original sample by the inclusion of the German DAX index that represents the mature European stock markets. The data employed in our study spans from January 2, 2008 to November 30, 2010, thus covers the period of the recent global financial crisis, from its outbreak to the early recovery phases. In the static analysis, we find the Czech stock market to transmit the highest amount of volatility shocks to the other markets what might be attributed to the potential role of the Czech market as a channel of volatility shocks transmission among the included and non-included stock markets. Furthermore, the results of dynamic analysis reveal the presence of asymmetry in...
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Monte Carlo simulation of Counterparty Credit Risk
Havelka, Robert ; Šopov, Boril (advisor) ; Skuhrovec, Jiří (referee)
The counterparty credit risk is particularly hard to simulate and this thesis is only the second work so far, which considers effective simulation of couterparty risk. There are two new approaches to stochastic modelling, which are useful with respect to ef- ficient simulation of counterparty risk. These are Path-Dependent Simulation (PDS) and Direct-Jump to Simulation date (DJS). It had been show that DJS is far more ef- fective, when it comes counterparty risk simulation of path-independent derivatives. We focus on a portfolio of interest rate swaps, which are effectively path-dependent. DJS approach yields estimates with much lower variance than PDS approach. But as expected, the DJS is also much more computationally intensive. The increase in computing time in majority of cases wipes out any gains in lower variance and PDS approach is shown to be more effective, when computing time is taken into account. We also show that in practice the convergence rate of Monte Carlo method signif- icantly underestimates the true reduction in variance, which can be achieved with increasing number of scenarios. JEL Classification C02, C15, C63, G01, G12, G32 Keywords Monte Carlo, CVA, Exposure, Variance Author's e-mail robberth.cz@gmail.com Supervisor's e-mail boril.sopov@gmail.com
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Multivariate Dependence Modeling using Copulas
Klaus, Marek ; Šopov, Boril (advisor) ; Gapko, Petr (referee)
Multivariate volatility models, such as DCC MGARCH, are estimated under assumption of multivariate normal distribution of random variables, while this assumption has been rejected by empirical evidence. Therefore, the esti- mated conditional correlation may not explain the whole dependence struc- ture, since under non-normality the linear correlation is only one of the de- pendency measures. The aim of this thesis is to employ a copula function to the DCC MGARCH model, as copulas are able to link non-normal marginal distributions to create corresponding multivariate joint distribution. The copula-based MGARCH model with uncorrelated dependent errors permits to model conditional cor- relation by DCC-MGARCH and dependence by the copula function, sepa- rately and simultaneously. In other words the model aims to explain addi- tional dependence not captured by traditional DCC MGARCH model due to assumption of normality. In the empirical analysis we apply the model on datasets consisting primarily of stocks of the PX Index and on the pair of S&P500 and NASDAQ100 in order to compare the copula-based MGARCH model to traditional DCC MGARCH in terms of capturing the dependency structure. 1
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Stability of the Banking Sector: Dependence Beyond Correlation
Fiala, Tomáš ; Šopov, Boril (advisor) ; Zelený, Tomáš (referee)
We analyze systemic risk of banks in countries of the so-called Visegrad Group (V4). Particularly, we focus on the relationship between a foreign mother and its local subsidiary which we compare to the relationship between subsidiaries in a given V4 country. We find that the systemic risk between two subsidiaries is higher than that between a mother and the respective subsidiary. In our analysis, we employ a technique stemming from a nonparametric multivariate Extreme Value Theory which is distribution free. Thus, our results are robust to heavy tails. Keywords Extreme value theory, systemic risk, financial stability, Visegrad Group, mother-subsidiary re- altionship Author's e-mail tomas.fiala@gjn.cz Supervisor's e-mail boril.sopov@gmail.com
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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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