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Estimations of risk with respect to monthly horizon based on the two-year time series
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Pešta, Michal (referee)
The thesis describes commonly used measures of risk, such as volatility, Value at Risk (VaR) and Expected Shortfall (ES), and is tasked with creating models for measuring market risk. It is concerned with the risk over daily and over monthly horizons and shows the shortcomings of a square-root-of-time approach for converting VaR and ES between horizons. Parametric models, geometric Brownian motion (GBM) and GARCH process, and non-parametric models, historical simulation (HS) and some its possible improvements, are presented. The application of these mentioned models is demonstrated using real data. The accuracy of VaR models is proved through backtesting and the results are discussed. Part of this thesis is also a simulation study, which reveals the precision of VaR and ES estimates.
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Cyber risk modelling using copulas
Spišiak, Michal ; Teplý, Petr (advisor) ; Baruník, Jozef (referee)
Cyber risk or data breach risk can be estimated similarly as other types of operational risk. First we identify problems of cyber risk models in existing literature. A large dataset consisting of 5,713 loss events enables us to apply extreme value theory. We adopt goodness of fit tests adjusted for distribution functions with estimated parameters. These tests are often overlooked in the literature even though they are essential for correct results. We model aggregate losses in three different industries separately and then we combine them using a copula. A t-test reveals that potential one-year global losses due to data breach risk are larger than the GDP of the Czech Republic. Moreover, one-year global cyber risk measured with a 99% CVaR amounts to 2.5% of the global GDP. Unlike others we compare risk measures with other quantities which allows wider audience to understand the magnitude of the cyber risk. An estimate of global data breach risk is a useful indicator not only for insurers, but also for any organization processing sensitive data.
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Estimations of risk with respect to monthly horizon based on the two-year time series
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Pešta, Michal (referee)
The thesis describes commonly used measures of risk, such as volatility, Value at Risk (VaR) and Expected Shortfall (ES), and is tasked with creating models for measuring market risk. It is concerned with the risk over daily and over monthly horizons and shows the shortcomings of a square-root-of-time approach for converting VaR and ES between horizons. Parametric models, geometric Brownian motion (GBM) and GARCH process, and non-parametric models, historical simulation (HS) and some its possible improvements, are presented. The application of these mentioned models is demonstrated using real data. The accuracy of VaR models is proved through backtesting and the results are discussed. Part of this thesis is also a simulation study, which reveals the precision of VaR and ES estimates.
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Risk aggregation allowing for skewness
Šimonová, Soňa ; Mazurová, Lucie (advisor) ; Zichová, Jitka (referee)
The main objective of this thesis is to examine different methods of calcula- tion of economic capital for an insurance company which allow for skewness. For calculating the economic capital we use two alternative risk measures- Value at Risk (VaR) and Conditional Value at Risk (CVaR). The first part of the thesis is concerned with deriving exact formulae for VaR and CVaR for normally distribu- ted losses and describing the modification of these formulae using Cornish-Fisher approximation. Next, the method using lognormal model with a parameter cap- turing skewness is discussed. The parameter is used for deriving a formula for skewness of a sum of losses. The approximation of the sum is thus obtained and is used for deriving formulae for VaR and CVaR for aggregated losses. Finally, the methods are compared numerically using R software. 1
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Optimization of reinsurace parameters in insurance
Dlouhá, Veronika ; Branda, Martin (advisor) ; Cipra, Tomáš (referee)
This thesis is dedicated to searching optimal parameters of reinsurance with a focus of quota-share and stop-loss reinsurance. The optimization is based on minimization of value at risk and conditional value at risk of total costs of the insurer for the recieved risk. It also presents a compound random variable and shows various methods of obtaining its probability distribution, for example ap- proximation by lognormal or gamma mixtures distributions or by Panjer recurive method for continuous severity and numerical method of its solution. At the end of the thesis we can find the calculation of the optimal parameters of reinsurance for a compound random variable based on real data. We use various methods to determine probability distribution and premiums. 1
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Alternative risk measures and their applications
Drobuliak, Matúš ; Hurt, Jan (advisor) ; Večeř, Jan (referee)
Title: Alternative risk measures and their applications Author: Matúš Drobuliak Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Jan Hurt, CSc., Department of Probability and Mathe- matical Statistics Abstract: The objective of this thesis is to discuss alternative measures of risk. We focused on the expectile value at risk, which we compared with conventional risk measures - namely value at risk and conditional value at risk. We also discussed its properties from the financial point of view. A numerical illustration is included in the thesis. Keywords: Value at risk, Conditional value at risk, Quantile, Expectile, Expectile value at risk iii
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Financial Risk Management - Comparison of Value at Risk Methods on Stock Portfolios
Yigiter, Yasin Cagri ; Žamberský, Pavel (advisor) ; Taušer, Josef (referee)
Recent developments in the financial sector and with the effects of globalization, restrictions on portfolio investments are in lowest in its history. These improvements help to facilitate fund transfer between countries, which causes high diversity and degree of risk. Also, this situation remarked itself in unexpected bankruptcies of major international financial institutions such as Barings Bank. As a result, international investors and academics forced to discover easy and efficient risk measurement techniques. Value at Risk method has emerged as a result of these requirements. Value at Risk is the maximum loss that value of an asset can experience with a given confidence level over a specific time frame. The purpose of this study compares the calculations of Value at Risk Methods, namely Variance- Covariance Method, Historical Simulation Method, and Monte Carlo Simulation Method. Firstly, ten stocks are chosen randomly from Istanbul Stock Exchange for the analysis. Descriptive statistics of these shares are calculated, to achieve final results. Secondly, normality tests are made to determine the distribution of return series. In the next step, optimal portfolio obtained according to Markowitz model. Finally, Value at Risk values of the optimal portfolio calculated with three different methods.
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Setting of the exposition limit for brokerage companies using risk quantifying methods
Nováková, Kateřina ; Zouhar, Jan (advisor) ; Holý, Vladimír (referee)
This thesis is focused on brokerage companies, the middlemen of investors' demands for buying and selling currency pair, and their problems of determining the proper limit on their currency exposition. The limit value has an influence on company's gains and losses resulting from exchange rate movement. The thesis describes a method how to quantify the risk of loss utilizing common financial indicators like Value at Risk and Expected Shortfall. The aim of the~thesis is to describe how to estimate these indicators. Real data supplied by brokerage company are used for calculation. The replication method is applied for determining the values of indicators, data for calculation are stochastically simulated. All calculations are implemented in R.
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Impacts of new regulatory requirements for market risk
Vojkůvka, Adam ; Witzany, Jiří (advisor) ; Brodani, Jana (referee)
The aim of this master thesis is analyze the impact of new regulatory requirements for market risk in terms of internal approach of the selected portfolio. The first part deals with the definition and calculation methods of risk measures Value at Risk and Expected Shortfall. Furthermore, this part is dedicated to model backtesting and determination of the stress period. The second part describes the development of Basel I-III regulatory requirements for market risk with a focus on internal approaches. The third part focuses on the calculation and subsequent analysis of current and new regulatory reguirements for market risk using the historical simulation method, variance and covariance method and Monte Carlo simulation.
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Possibilities and Methods of Exchange Rate Risk Management
Cheuzova, Olga ; Brůna, Karel (advisor) ; Marková, Jana (referee)
The subject of this bachelor thesis Possibilities and Methods of Exchange Rate Risk Management is to understand how the exchange rate risk arises and how it can be managed, analysis of methods and options of exchange rate risk management and determination of exchange rate risk by the international stock company Orco Property Group S.A. which eliminates the unfavorable impacts of the development of individual of the functional currencies of the subsidiaries on the consolidated balance sheet. The first part focuses on the understanding of the course risk management process from a theoretical point of view. The second part introduces Orco, its financial analysis, analysis of its foreign exchange exposure and currency risk management.
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