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Stressed Value-at-Risk: Assessing extended Basel II regulation
Pižl, Vojtěch ; Šopov, Boril (advisor) ; Avdulaj, Krenar (referee)
This thesis investigates recently proposed enhancements to the Basel II market risk framework. The Basel Committee on Banking Supervision introduced a stressed Value-at-Risk, calculated from one year long period of financial stress, to be added to the current VaR as a reaction to the shortage in capital reserves of banks and thus their inability to cover extensive losses observed during the recent crisis. We present an empirical evidence that such an extension of the regulatory capital is not optimal. Firstly, supplementing an unconditional methods of VaR estimation, i.e. normal parametric VaR and historical simulation, by SVaR only lead to unnecessarily high capital requirements even in a low volatile periods whilst the same amount of capital during the crisis could be achieved using either the conditional GARCH VaR with student's-t innovations or the volatility weighted historical simulation. Moreover, we showed that all unconditional methods fail to capture volatility clusters such as the 2008 crisis.
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Price elasticity of household water demand in Czech Republic
Hortová, Jana ; Krištoufek, Ladislav (advisor) ; Šopov, Boril (referee)
Během posledních desetiletí se v eské republice stále zvyšují ceny vody, což vede k následnému snižování její spotřeby. Tomuto tématu se věnuje velké množství studií, ale dle našich zjištění se žádná z nich nezabývá eskou republikou. Obecně lze říci, že hlavním cílem této práce je nalezení krátkodobé a dlouhodobé cenové elasticity poptávky po vodě v eské republice a následně v Kladně. Při zkoumání poptávky po vodě v Kladně vyšetřujeme cenovou elasticitu v závislosti na odlišném počtu člen· v domácnostech. V obou případech dojdeme k závěru, že poptávka je neelastická v krátkém i dlouhém časovém období. Dále zjistíme, že cenová elasticita roste s klesajícím počtem člen· domácností v obou časových obdobích. Naše výsledky jsou v souladu se závěry ostatních studií.
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Reduced-form approach to LGD modelling
Hlavatá, Ivana ; Seidler, Jakub (advisor) ; Šopov, Boril (referee)
The master thesis deals with the advanced methods for estimating credit risk parameters from market prices: probability of default (PD) and loss given default (LGD). Precise evaluation of these parameters is important not only for banks to calculate their regulatory capital but also for investors to price risky bonds and credit derivatives. We provide forward looking reduced-form analytical method for calculation of PD and LGD of corporate defaultable bonds based on their quoted market prices, prices of equivalent risk-free bonds and quoted credit default swap spreads of the issuer of these bonds. This is reversed to most of the studies on credit risk modeling, as aim is not to price instruments based on estimated credit risk parameters, but to calculate these parameters based on the available market prices. Furthermore, compared to other studies, the LGD parameter is assumed to be endogenous and we provide the method for its simultaneous calculation with the probability of default. Finally, using developed methods, we estimate implied PD and LGD for five European banks assuming that the risk is priced correctly by other investors and the markets are efficient. JEL Classification: C02, C63, G13, G33 Keywords: credit risk, loss given default, probability of default, credit default swap Author's...
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Extreme value theory: Empirical analysis of tail behaviour of GARCH models
Šiml, Jan ; Šopov, Boril (advisor) ; Kocourek, David (referee)
This thesis investigates the capability of GARCH-family models to capture the tail properties using Monte Carlo simulation in framework of Conditional Extreme Value Theory. Analysis is carried out for three different GARCH-type models: GARCH, EGARCH, GJR-GARCH using Normal and Student's t-distributed innovations on four well-known stock market indices: S&P 500, FTSE 100, DAX and Nikkei 225. After conducting 3000 simulations of every estimated model, the Hill estimate of shape parameter implied by the GARCH-type models will be calculated and the models' performance will be assessed based on histograms, descriptive statistics and Root Mean Squared Error of simulated Hill estimates. Interesting results and im- plications for further research have been identified. Firstly, we highlight the Normal distribution's inappropriate nature in this case and its inability to capture the tail properties. Furthermore, GJR-GARCHT with t-distributed innovations is identified to be the best model, closely followed by other t-distributed GARCH-type models. Finally, a pattern in all Q-Q plots forecasting the simulation study results is appar- ent, with the exception of the DAX. This anomalous behaviour therefore necessitated further analysis and a significant right tail influence was recorded. Even though Hill estimates...
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Reduced-form Approach to LGD Modeling
Hlavatá, Ivana ; Seidler, Jakub (advisor) ; Šopov, Boril (referee)
The rigorous thesis deals with the advanced methods for estimating credit risk parameters from market prices: probability of default (PD) and loss given default (LGD). Precise evaluation of these parameters is important not only for banks to calculate their regulatory capital but also for investors to price risky bonds and credit derivatives. We develop two forward looking reduced-form analytical methods for calculation of PD and LGD of corporate defaultable bonds based on their quoted market prices, prices of equivalent risk-free bonds and quoted senior and subordinated credit default swap spreads of the issuer of these bonds. This is reversed to most of the studies on credit risk modeling, as aim is not to price instruments based on estimated credit risk parameters, but to calculate these parameters based on the available market quotes. Furthermore, compared to other studies, the LGD parameter is assumed to be endogenous and we provide the method for its simultaneous calculation with the probability of default. Finally, using developed methods, we estimate implied PD and LGD for nine European banks assuming that the risk is priced correctly by other investors and the markets are efficient. JEL Classification: C02, C63, G13, G33 Keywords: credit risk, loss given default, probability of default,...
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Income Elasticity of Money Demand: A Meta-Analysis
Sedlaříková, Jana ; Havránek, Tomáš (advisor) ; Šopov, Boril (referee)
The income elasticity of money demand represents an important economic variable which affects money demand function. Precise evaluation of money demand is important for central banking and for determining the transmission mechanism. Nevertheless, there is no general agreement on the exact structure of the function of money demand and income elasticity values neither in theoretical nor practical context. Many different economic theories concerning this field were developed by various economists during the 20th century. There was also a large amount of empirical research whose goal was to estimate the value of income elasticity based on real economic data. However, these studies are characterized by strong heterogeneity of the respective results. The method of meta-analysis is considered to be an effective statistical instrument that allows systematic evaluation of these inconsistent estimates. This method was applied to the dataset consisting of 985 empirical estimates from more than 70 primary studies. The publication selection bias was detected only in the case of using broad monetary aggregates. The resulting estimates adjusted for publication bias range from 0.784 for narrow monetary aggregates to 0.93 for the broadly defined money. In addition, meta- regression analysis revealed correlation...
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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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Analysis of stock market anomalies: US cross-sectoral comparison
Jílek, Lukáš ; Krištoufek, Ladislav (advisor) ; Šopov, Boril (referee)
The purpose of this thesis is to analyze anomalies in the US stock market. Special attention is put on Day of the week effect, January effect, and Part of the month effect. We focus on comparison of companies with low and high capitalization. We perform an analysis across 6 major industrial sectors. Then, we discuss the findings with results of past projects and finally, we try to find a speculative investment strategy. We found out that neither Day of the week effect nor January effect do not appear in US stock market nowadays. Part of the month effect was the only anomaly, which was observed in our data. Keywords Stock market anomalies, financial markets, cross-sectoral analysis, Jannuary effect, Day of the week effect, Part of the month effect Author's e-mail jileklukas@gmail.com Supervisor's e-mail kristoufek@gmail.com
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Analysis of gasoline and diesel prices in the Czech Republic
Badáňová, Martina ; Krištoufek, Ladislav (advisor) ; Šopov, Boril (referee)
This thesis investigates relationship between fuel (gasoline and diesel) prices in the Czech Republic and world crude oil prices over the period from 2004 to 2011. Using daily data we estimate an asymmetric error correction model and we find that in the short-run fuel prices are adjusted upwards to the long-run equilibrium faster than they are adjusted downwards to the equilibrium. However, the difference in responses is found to be not statistically significant.
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Financial Risk Measures: Review and Empirical Applications
Říha, Jan ; Šopov, Boril (advisor) ; Krištoufek, Ladislav (referee)
This thesis focuses on several classes of risk measures, related axioms and properties. We have introduced and compared monetary, coherent, convex and deviation classes of risk measures and subsequently their properties have been discussed and in selected cases demonstrated on data. Furthermore the relatively promising and advanced class of risk measures, the spectral risk measures, has been introduced. In addition to that we have outlined selected topics from portfolio theory that are relevant for applications of selected risk measures and then derived theoretical solution of portfolio selection using chosen risk measures. In the end we have highlighted the potential consequences of improper employment of certain risk measures in portfolio optimization.
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