|
|
Application of Monte Carlo simulation in risk management
Pelešková, Kateřina ; Teplý, Petr (advisor) ; Stádník, Bohumil (referee)
The global financial crisis of 2008, which forced the central banks around the world to defend a financial stability by using non-standard instruments such as quantitative easing, has resulted in, among other things, the fall of the interest rates to zero, and even to negative values in some countries, which has become the new normal in banking field. In this thesis, we focused on the Czech financial market, and we used the method of Monte Carlo simulation in the Vasicek model for the prediction of the future development of interest rates, both short and long maturities. The model shows that in the short term the rates may fall to negative values, but the prediction shows rising interest rates up to their own equilibrium. The 3-months and 6-months rates show surprisingly uncharacteristic behavior, where their long-term decline and higher volatility caused calculation of the equilibrium as a negative value in the Vasicek model. Than we apply the results in the model for calculating changes in the prices of bonds, which are negatively correlated with the interest rates, and we explore the repricing costs for the bondholders. Also, we will show that commercial banks may control the impact of the interest rate risk on capital by composition of financial assets in various categories, where the accounting classification of the instrument is critical to revaluation of the capital.
|
|
|
Valuation of employee stock options in accordance with IFRS 2 at fair value basis
Červený, Martin ; Mařík, Miloš (advisor) ; Strouhal, Jiří (referee)
This master's thesis is dealing with the topic of employee stock options (ESOs), primarily with the valuation of ESOs in accordance with the accounting standard IFRS 2 at corresponding fair value basis. The goal of this thesis is a critical analysis of the standard mentioned, with respect to the conditions of the Czech Republic. The theoretical part comes with the basic characteristics of employee stock options and explains how the traditional option-valuation models can be modified for the purpose of ESOs valuation. It is also concerned with discussion about fundamental features of the fair value basis necessary for the valuation process. The essential part of this thesis is the critical analysis focusing on the rationality of accounting methods, disclosure requirements and also on a theoretically correct determination of model inputs. Critical analysis is followed by case study aimed on evaluation of an authentic option plan. The practical part also demonstrates advanced methods of valuation using the Black-Scholes and the binominal models as well as the Monte Carlo simulation. In the conclusion, I present proposals for changes of the IFRS 2. According to the results of the critical analysis, supported by case study, greatest shortcomings were identified in the disclosure requirements. Proposals for changes are aimed mainly on this problem.
|
|
|
Analysis of variance in R
Švejdová, Klára ; Matějka, Martin (advisor) ; Sobíšek, Lukáš (referee)
The bachelor thesis focuses on the One-way ANOVA and its nonparametric counterpart the Kruskal-Wallis test. The aim of this bachelor thesis is to analyse the ANOVA's test validity and power in case of assumptions (e. g. normal distribution, homoscedasticity and sample size) violations. The conclusions of the One-way ANOVA are compared with the Kruskal-Wallis test. The analysis is performed using Monte Carlo simulations implemented in the statistical software R. Based on the simulations, it is found out that the One-Way ANOVA is not significantly sensitive to the violation of normality, if the homoscedasticity assumption is met within each of four samples. On the other hand it is found out that the One-Way ANOVA is significantly sensitive to the violation of homoscedasticity at the particular specification. The Kruskal-Wallis test yields in better results if the homoscedasticity assumption is violated. In case that the One-Way ANOVA and the Kruskal-Wallis test are valid, the ANOVA provides higher power of the test.
|
|
|
Business risks in insurance and their quantification
Szarková, Lucia ; Ducháčková, Eva (advisor) ; Oborilová, Mária (referee)
Diploma thesis Business risks in insurance and their quantification describes the business risks to which insurance companies are exposed in their activities. Thesis is focused on market risk and quantification of market risk in insurance companies. It includes determination of the specifications for the activities of insurance companies, regulation and characteric of business risks in insurance. Large part of the thesis deals with the method of Value at Risk as a tool to measure market risk as well as individual methods to calculate it. In the conclusion, thesis describes the processes of quantification of market risk in Generali PPF Holding and in Česká poisťovňa, which gives a practical insight into the issues of market risk in insurance companies.
|
|
|
Capital protected funds
Houdek, Ondřej ; Witzany, Jiří (advisor) ; Prokop, Martin (referee)
This thesis is mainly focused on pricing securities of selected capital protected funds. In its theoretical part, there are summarized approaches and principals that are generally used for derivatives pricing because capital protected funds' securities contain embedded options. Emphasis is put on risk-neutral pricing using Monte Carlo simulation at that point because complicated pay-off functions of these funds are hard to be evaluated analytically. There are also presented main approaches to constructions and portfolio management of these funds from their portfolio manager's viewpoint. Finally, there is made an overview of basic types of capital protected funds issued both in The Czech republic and Europe. Analytical part is focused on evaluation of selected capital protected funds. There is applied a standard approach that is based on a simulation of Geometric Brownian Motion with constant conditional variance and correlation in contrast with an advanced approach where the conditional variance and conditional correlation matrix are simulated as well. That is accomplished with GARCH-in-mean and DCC-GARCH models. Estimated prices are compared with real market prices and there is also performance of the standard models compared with performance of advanced ones.
|
|
|
Option strategies
Foukal, Viktor ; Witzany, Jiří (advisor) ; Baran, Jaroslav (referee)
The main objective of this thesis is to acquaint the reader with the main types of option strategies, with the principles of functioning, with the methods of creating and analyzing these strategies. The practical part focus on valuation of tested option strategies, determination of the conditions for entry into strategies, prediction of future development of index S&P 500 by Monte Carlo simulation and finding relation between implied volatility of options and underlying asset itself.
|
|
|
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.
|
|
|
Analysis of guaranteed investment funds
Mach, Jonáš ; Witzany, Jiří (advisor) ; Stádník, Bohumil (referee)
This thesis focuses on guaranteed investment funds, which have become very popular among investors in the Czech Republic in recent years. The reason for this popularity is the conservativeness of a typical domestic investor, who appreciates the lower bound for the value of his investment. Guaranteed funds characteristically have a complex structure and valuation of their profitability based solely on intuition is therefore impossible. This analysis tries to provide an answer to the question if investing in these funds is reasonable. A large part of the thesis is dedicated to the option theory and option valuation methods, including the famous Black-Scholes formula, as guaranteed investment funds have the characteristics of an option. Thanks to the complicated structure of these products, the analysis itself is done by Monte Carlo simulation.
|
|
|
Comparison of simulation programs and their application
Krupa, Martin ; Kuncová, Martina (advisor) ; Řezanková, Hana (referee)
Abstract (eng): This diploma paper compares available software for simulations. These are MATLAB, WITNESS, SIMUL8, SIMPROCESS and CRYSTAL BALL. In the first part, the dynamic simulations are explained, its methodic, purpose, areas of implementation and after that it describes the simulation of Monte Carlo type. These are the basic types of simulations used by programs mentioned in this paper. After a short introduction follows detailed description of the system requirements, user interface and the principles of working with these programs, that contains also a definition of basic function blocks. This paper also describes another important information like price, available licenses and in the attachment the pictures of the programs interface. The next part of my paper is based on analyze of observed articles, which concern this special area of interest. I try to describe the usage of this software on a market, area of application or eventually a type of simulation. The information from data assimilation are ordered in transparent tables and visualized on a graphs and diagrams. At the end is the final summary, which I believe will be beneficiary for the readers.
|
|
|
Derivative Pricing Using Monte Carlo Simulations
Burešová, Jana ; Witzany, Jiří (advisor) ; Málek, Jiří (referee)
Pricing of more complex derivatives is very often based on Monte Carlo simulations. Estimates given by these simulations are derived from thousands of scenarions for the underlying asset price developement. These estimates can be more precise in case of higher number of scenarions or in case of modifications of a simulation mentioned in this master thesis. First part of the thesis includes theoretic description of variance reduction techniques, second part consists of implementation of all techniques in pricing a barrier option and of their comparison. We conclude the thesis by two statements. The former one says that usage of each technique is subject to simulation specifics, the latter one recommends to use MC simulations even in the case a closed-form formula was derived.
|
guest ::
