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Extreme Value Theory in Operational Risk Management
Vojtěch, Jan ; Kahounová, Jana (advisor) ; Řezanková, Hana (referee) ; Orsáková, Martina (referee)
Currently, financial institutions are supposed to analyze and quantify a new type of banking risk, known as operational risk. Financial institutions are exposed to this risk in their everyday activities. The main objective of this work is to construct an acceptable statistical model of capital requirement computation. Such a model must respect specificity of losses arising from operational risk events. The fundamental task is represented by searching for a suitable distribution, which describes the probabilistic behavior of losses arising from this type of risk. There is a strong utilization of the Pickands-Balkema-de Haan theorem used in extreme value theory. Roughly speaking, distribution of a random variable exceeding a given high threshold, converges in distribution to generalized Pareto distribution. The theorem is subsequently used in estimating the high percentile from a simulated distribution. The simulated distribution is considered to be a compound model for the aggregate loss random variable. It is constructed as a combination of frequency distribution for the number of losses random variable and the so-called severity distribution for individual loss random variable. The proposed model is then used to estimate a fi -nal quantile, which represents a searched amount of capital requirement. This capital requirement is constituted as the amount of funds the bank is supposed to retain, in order to make up for the projected lack of funds. There is a given probability the capital charge will be exceeded, which is commonly quite small. Although a combination of some frequency distribution and some severity distribution is the common way to deal with the described problem, the final application is often considered to be problematic. Generally, there are some combinations for severity distribution of two or three, for instance, lognormal distributions with different location and scale parameters. Models like these usually do not have any theoretical background and in particular, the connecting of distribution functions has not been conducted in the proper way. In this work, we will deal with both problems. In addition, there is a derivation of maximum likelihood estimates of lognormal distribution for which hold F_LN(u) = p, where u and p is given. The results achieved can be used in the everyday practices of financial institutions for operational risks quantification. In addition, they can be used for the analysis of a variety of sample data with so-called heavy tails, where standard distributions do not offer any help. As an integral part of this work, a CD with source code of each function used in the model is included. All of these functions were created in statistical programming language, in S-PLUS software. In the fourth annex, there is the complete description of each function and its purpose and general syntax for a possible usage in solving different kinds of problems.
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Hedging currency risks in the context of Czech export
Renč, Jan ; Žamberský, Pavel (advisor) ; Šaroch, Stanislav (referee)
The main focus of this work is on hedging of currency risks with special emphasis on the case of Czech export. In the first chapter, I create a motivation for further studying of the problem. I describe the state of export industries and the economy as a whole and how these aspects are connected to the exchange rates. In the second chapter, I explain how firms create their assumptions about future exchange rates. I also run a Monte Carlo analysis on historical data and come with predictions of my own. In the third chapter, I am discussing the relevance of using VaR models for estimating the maximum possible loss of funds due to unwanted moves in the exchange rate. Furthermore, I describe various instruments usable for hedging of currency exposure including forwards, options, swaps and other derivatives. In the final chapter of this work, I am asking financial and sales directors of 51 Czech firms about how currency risks influence their businesses and how they protect themselves against these threats.
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Selected aspects of market risk management
Cao, Bien Thuy ; Blahová, Naděžda (advisor)
The main objective of the bachelor thesis is to define the basic methods for measurement and a way to reduce market risk. In the beginning of work the basic types of financial risk are defined, then individual types of market risk are described in more detail. Next the methods Value at risk for measuring market risk -- the method of variation and covariance, historical simulation and Monte Carlo simulation -- are explained. To specify measurement of interest-rate risk gap analysis and duration gap analysis are analyzed. Then there is enlightened about financial derivatives, which serve as the basic tools to ensure market risk. Therewithal standardized method for calculating capital requirements for various market risks is developed. Theoretical knowledge gained by studying literature is applied in the calculation of VaR by the method of variation and covariance. And triangular decomposition principle is used to influence the value at risk.
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Application of Value at Risk method on market risk management
Vostatek, Jan ; Witzany, Jiří (advisor) ; Witzany, Jiří (referee)
The bachelor's thesis is focused on the Value at Risk method which is widely used for management of market risk. Value at Risk is put in the whole risk management framework and it is explained its application on the two of three main ways of calculation. The thesis also deals with the role of Value at Risk in regulatory rules of European Union and possible future development of market risk regulation of financial institutions. Some chapters of the thesis describe the application of Value at Risk on economic capital allocation and setting limits on trading desks. At the end of the thesis Value at Risk is deeply evaluated in respect of all relevant information.
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Development of the concept of the capital adequacy in the Slovak banking sector
Cipková, Dagmara ; Půlpánová, Stanislava (advisor)
This bachelor thesis deals with the analysis of the development of the capital adequacy in the Slovak republic. It describes the adaptation of the calculation of the capital adequacy on the basis of the Basel I treatment, which gradually transforms into the Basel II methods, and briefly describes the new upcoming adaptation. The main body of this work consists of the methods for calculating the credit, the market and the operational risk, and the determination of capital requirements. Particular methods are described according to the individual adaptations in attention of the sequence exploitation. An attention is also paid to the short description of the three pillars of the Basel II. Global trend is supplemented by the information from the banking sector.
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Managing financial risks in an insurence company
Čech, Tomáš ; Marek, Luboš (advisor) ; Branda, Martin (referee)
The graduation thesis addresses the problems of managing and measuring of financial risks in activities of insurance companies. The first chapter handles the definitions of the financial risk and it classification. The second chapter defines a random variable returns of measure of financial assets. Sets up formulas of the return measure and also focuses on problem of time aggregation. The third chapter theoretically describes methodology of value at risk as the most widely used method for measuring and managing risk by insurance companies and regulatory authority. The fourth chapter contains an empirical study from practice which compares the two basic method of computing value at risk. The fifth chapter is the main part of the graduation thesis and focuses on verifying of the model and his imperfections. It verifies also achievements of initial assumptions. The sixth chapter targets on possibilities of extension value at risk method by liquidity risk incorporation.
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Use of Derivatives in International Trade in Agricultural Commodities
Plchotová, Jitka ; Sedláček, Jiří (advisor) ; Chalupa, Leoš (referee)
The aim of this diploma thesis is to theoretically describe the risks connected to entrepreneurship. Stress is put mainly on financial risks that are related to price shifts of agricultural commodities and to changes in the exchange rates. The basis lies in theoretical identification of the nature of possible risks, methods of risk evaluation and description of instruments that serve for the risk elimination. This theoretical knowledge is further applied in case studies dealing with hedging of commodity and currency risks of firms that conduct business in agricultural basic industry. The analysis of firm's position, demonstration of hedging and final evaluation of efficiency are included.
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Methods of the calculation of Value at Risk for the market and credit risks
Štolc, Zdeněk ; Witzany, Jiří (advisor) ; Paholok, Igor (referee)
This thesis is focused on a theoretical explication of the basic methods of the calculation Value at Risk for the market and credit risk. For the market risk there is in detail developed the variance -- covariance method, historical simulation and Monte Carlo simulation, above all for the nonlinear portfolio. For all methods the assumptions of their applications are highlighted and the comparation of these methods is made too. For the credit risk there is made a theoretical description of CreditMetrics, CreditRisk+ and KMV models. Analytical part is concerned in the quantification of Value at Risk on two portfolios, namely nonlinear currency portfolio, which particular assumptions of the variance -- covariance method a Monte Carlo simulation are tested on. Then by these methods the calculation of Value at Risk is realized. The calculation of Credit Value at Risk is made on the portfolio of the US corporate bonds by the help of CreditMetrics model.
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