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Financial Analysis of CDO Structures
Dvořáková, Jitka ; Myška, Petr (advisor) ; Bartoš, Milan (referee)
This thesis deal with structured products which term is Collateralized Debt Obligations. Thesis describe mechanism, how this structures are working, pricing methods, which are using copula function and solve problems with choise of collateral pool, which substantially determine results of quantitative analysis of this products. Finally are these methods and results of quantitative analysis applied to the fictive collateral pool.
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One factor models of interest rates
Jambor, Matúš ; Myška, Petr (advisor) ; Hurt, Jan (referee)
Title: One factor interest rate models Author: Matúš Jambor Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Petr Myška Abstract: In this thesis we looked closely at the models of interest rates that are applied in the area of financial mathematics and actuarial sciences. There are several models that try to describe the behavior of yield curve plausibly. In most of the cases the models stem from probability theory and coincidence. These models are also means for assessment of financial derivates whose price de- pends on the interest rates movements. The work deals with three one-factor models which are analyzed into more details in the second chapter. The last chapter is about real-data calibration. Keywords: one factor models, interest rates, maximum likelihood method 1
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Calculation of capital requirements of market risk for options on stock's basket
Lendacký, Peter ; Myška, Petr (advisor) ; Večeř, Jan (referee)
The goal of the paper is to compare different approach in calculation of capital requirement of market risk for options on stock's basket and describe their impact on selected instrument. The first part of the paper describes possible approaches for the capital requirement calculation, namely Standardized approach and Internal model approach, and the theoretical base for option pricing. An instrument with the embedded option on equities was chosen to show the impact. Although the instrument is valued using Monte Carlo simulation, one chapter is devoted to Black-Scholes model as the base model for option pricing. Powered by TCPDF (www.tcpdf.org)
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Stress testing in quantitative analysis of securitized products
Maťašová, Dominika ; Myška, Petr (advisor) ; Mandl, Petr (referee)
In the present work we study the securitized products of financial markets with focus on collateralized debt obligations. In first part the thesis deals with the reasons behind launching these products, the portfolio, tranches and further on mechanisms how these structures are working. In the second part the thesis describes the valuation methods for which the Markov chains and copula functions are used. Further on follows the practical part with output from the quantitative analysis and at the end the thesis describes the stress testing of particular parametres.
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Valuation of Credit Derivatives
Davidová, Věra ; Witzany, Jiří (advisor) ; Myška, Petr (referee)
Credit derivatives are very interesting financial instrument both theoretically and practically. Their valuation has become an often discussed topic during the financial crisis since 2007. First part of this work is dedicated to standard types of credit derivatives, mainly to description of their character and to information about the historical development and also about the actual situation on the credit derivative market. However, this work is primarily focused on valuation of more complicated credit derivatives, namely Collateralized Debt Obligation (CDO), where modeling of correlation between underlying assets is required e.g. by copula functions. Then it deals with the mechanism of allocation of cash flow from underlying portfolio to CDO debt tranches, which is called financial waterfall. The goal of this work is to estimate price of a derivative by simulation methods and to examine an impact of changes in correlation structure inside portfolio, in recovery rates of assets and in other parameters of valuation. This valuation runs on real data about traded derivative, so it can be compared to its market value.
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Hypothesis Testing of interest rates models
Petrík, Daniel ; Myška, Petr (advisor) ; Hurt, Jan (referee)
V předložené práci se zabýváme problematikou stochastického modelování úro- kových sazeb. Jedním z nejobvyklejších postup· je modelovat dynamiku úroko- vých sazeb pomocí stochastické diferenciální rovnice difúze, jejímiž základními kameny jsou funkce driftu a funkce difúze. Od 70. let 20. století byla navržena celá řada model· tohoto typu, a ačkoli se tyto modely neustále zdokonalují, vyvstává přirozená otázka, zda se historicky pozorované úrokové sazby skutečně takovými difúzními rovnicemi řídily. V této práci budeme právě uvedenou hypo- tézu testovat pro několik nejběžnějších jednofaktorových model· úrokové sazby první generace. Z historických dat odhadneme obecnou momentovou metodou a metodou maximální věrohodnosti parametry jednotlivých difúzních rovnic a následně provedeme statistické testy dobré shody proložení těchto rovnic pozo- rovanými daty. 1
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Kreditní přirážka k tržnímu ocenění: přístupy k výpočtu a modelování
Mlej, Peter ; Witzany, Jiří (advisor) ; Myška, Petr (referee)
In this work we are introducing a risk neutral valuation formula for counterparty default risk adjustments in an unilateral and in a bilateral case. In the unilateral case the adjustment is represented by a Credit Valuation Adjust- ment(CVA) and in the bilateral case the adjustment is quantified by a Bilateral Risk Adjustment(BVA). We are incorporating these adjustments into the values of zero coupon bonds, coupon bearing bonds and interest rate swaps. For such an incorporation, risk neutral default probabilities extracted from the market quotes of Credit Default Swaps are needed. A Bootstrap method is used to derive them and a reduced form approach is used to model the default times. In the practical part, we are calculating Greek and Czech risk neutral default probabilities during the years 2008-2010. We are calculating CVA for 18 quoted Greek government bonds and we are comparing the adjusted prices with the market quoted prices of these bonds. We study the impact of a risk free interest rate curve choice on such a valuation. In the last sections, we construct an interest rate swap between the Czech and the Greece. We compute and study CVA and BVA for this interest rate swap.
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Optimalizace marže vkladových produktů banky
Hejmová, Barbora ; Hanuš, Martin (advisor) ; Myška, Petr (referee)
In the presented work we study xing of term deposit margins on Czech deposit market. Financial crisis which in fluenced almost each financial system hit also Czech banks. It resulted in almost no trading on interbank market and banks started to hoard liquidity from primary deposits. At the beginning of the thesis we introduce origin and expansion of liquidity crisis. Next we introduce term deposits and their basic properties on Czech deposit market. Then work is focused on term deposits and on xing their margins in dependence on several factors. Next part introduce model for optimal margin in dependence especially on demand for term deposits and competitive margin. There is also description of crisis impacts on suggested model. Results are built on term deposit of one of the largest banks on Czech deposit market. Data cover period from 2006 to 2008.
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