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Discrete versions of continuous financial models
Graeber, Jiří ; Hurt, Jan (advisor) ; Zahradník, Petr (referee)
This thesis studies the continuous-time financial models and their discrete versions, used for simulations and parameters estimations. Firstly, various stock price development and interest rates models are introduced. As a result of their uncertain future dynamics, these are defined as continuous-time stochastic processes. Secondly, a summary of discrete versions of continuous-time models, formed by Euler and Milstein discretization schemes, i.e. two most frequent ways of approximating a time-continuous stochastic process, is looked at. According to these discrete versions, simulations with different parameters are conducted in the third part of the thesis in order to illustrate individual behaviour of these models. In the conclusion, a comparison of a unique trajectory specified by the real data of one year interest rates swaps and of the simulations of Vasicek and Cox-Ingersoll-Ross model with parameters estimated from the real data is shown.
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Barrier options pricing
Macháček, Adam ; Witzany, Jiří (advisor) ; Hurt, Jan (referee)
In the presented thesis we study three methods of pricing European currency barrier options. With help of these methods we value selected barrier options with underlying asset EUR/CZK. In the first chapter we introduce the basic definitions from the world of financial derivatives and we describe our data. In the second chapter we deal with the classical model based on geometric Brownian motion of underlying asset and we prove a theorem of valuating Up-In-barrier option in this model. In the third chapter we introduce a model with stochastic volatility, the Heston model. We calibrate this model to market data and we use it to value our barrier options. In the last chapter we describe a jump diffusion model. Again we calibrate this jump diffusion model to market data and price our barrier options. The aim of this thesis is to decribe and to compare different methods of valuating barrier options. 1
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Financial risks with copulas
Prelecová, Natália ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The aim of this thesis is the thorough description of the copula theory. It deals with the theory's basic definitions, classes and characteristics. In addition, relations between copulas and dependence measures are explained. Furthermore, we evaluate the possibilities of copula's parametres estimation and selecting the right copula for real data. Then, the copula theory is interconnected with the basic risk measures in finance. We describe the elementary categorization of financial risks and standard risk measurement approaches. We also define basic risk measures with the emphasis on value at risk. Lastly, we present a real data case study of a selected portfolio.
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Stochastic interest rates modeling
Černý, Jakub ; Witzany, Jiří (advisor) ; Hurt, Jan (referee)
Title: Stochastic interest rates modeling Author: Jakub Černý Abstract: This present work studies different stochastic models of interest rates. Theoretical part of this work describes short-rate models, HJM fra- mework and LIBOR Market model. It focuses in detail on widely known short-rate models, i.e. Vašíček, Hull-White and Ho-Lee model, and on LI- BOR Market model. This part ends by valuation of interest rate options and model calibration to real data. Analytical part of the work analyses valuation of real non-standard interest rate derivative using different models. Part of this derivative valuation is comparison among models in terms of general valuation and also in terms of capturing the dynamics of interest rates. The aim of this work is to describe different stochastic models of interest rates and mainly to compare them with each other.
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Stochastic processes in the combination of life insurance and mortgage
Kalendovský, Jan ; Rotkovský, Martin (advisor) ; Hurt, Jan (referee)
The goal of the diploma thesis is to describe stochastic processes in the combination of mortgage loan and fund-linked life insurance, and to construct and analyze suitable mathematical models related to them. The idea of the combination of mortgage loan and fund-linked life insurance consists in serving the debt via paying up the interest only and investing the rest of the instalment within a fund-linked life insurance, instead of amortizing the debt gradually. At the maturity time, the principal sum will be amortized at once, using assets which have been invested within a fund-linked life insurance.
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Mortgage Bonds
Matuštík, Ondřej ; Bartoš, Milan (advisor) ; Hurt, Jan (referee)
Nazev prace: Dluhopisy zajistene aktivy (ABS) Autor: Ondfej Matustik Katedra: Katcdra pravdepodobnosti a matematicke statistiky Vedouci diplomove prace: Mgr. Milan BartoS E-mail vedouciho: mbartos@csas.cz Abstrakt: Diplomova prace se zabyva cennymi papiry krytymi aktivy (Asset backed securities, ABS). PodrobnC popisuje jejich strukturu a jejich procesni zpracovani, kterc se nazyva sekuritizace. Dale obsahuje pojednani o specialnich spolecnostech (SPY), ktere jsou pro cenne papiry krytc aktivy klicove. Prace rozebira faktory, kterc z velkc casti ovlivnuji proces sekuritizace, a ukazuje, za jakych podmfnek se vyplati emitovat cenne papiry kryte aktivy. Podrobne je zpracovan model sekuritizace vyrobniho podniku, kde jsou budouci vynosy a naklady modclovany pomoci nahodnych velicin. V dalsi casti popisuje sekuritizaci ccnnych papiru. Detailne se zabyva jejich ratingcm a pravdepodobnosti defaullu. Pozornost je venovana i modelu sekuritizace homogenniho souboru aktiv. V prakticke casti je prace zamefena na model fmancovani vystavby jaderne elektrarny pomoci cennych papiru krytych aktivy, Podrobne rozebira naklady a vynosy jaderne elektrarny. Tyto veliciny jsou pomoci nahodnych velicin simulovany pro odhad budoucich cash flow jaderne elektrarny. Vysledky pomahaji rozhodovat pfi koupi cennych papiru krytych vynosy...
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Quantitative Methods of Risk Control
Marcinek, Daniel ; Hurt, Jan (advisor) ; Hendrych, Radek (referee)
This thesis deals with stock modelling using ARCH and GARCH time series. Important aspect of stock modelling is to capture volatility correctly. Volatility in finance is usually defined as a standard deviation of asset returns. Many different models, which are summarized in the first part of this thesis, are used to model volatility. This thesis focus on multivariate volatility models including multivariate GARCH models. An approach to constructing a conditional maximum likelihood estimate to these methods is given. Discussed theory is applied on real financial data. In numeric application there is a construction of a volatility estimates for two specific stocks using models described in the first part of this thesis. Using the same financial data various bivariate models are compared. Based on comparison using maximum likelihood a specific model for these stocks is recommended. Powered by TCPDF (www.tcpdf.org)
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