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Option pricing with stochastic volatility
Bartoň, Ľuboš ; Málek, Jiří (advisor) ; Witzany, Jiří (referee)
This diploma thesis deals with problem of option pricing with stochastic volatility. At first, the Black-Scholes model is derived and then its biases are discussed. We explain shortly the concept of volatility. Further, we introduce three pricing models with stochastic volatility- Hull-White model, Heston model and Stein-Stein model. At the end, these models are reviewed.
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Jednorozměrné difusní stochastické diferenciální rovnice s aplikacemi ve finanční matematice
Zahradník, Petr ; Štěpán, Josef (advisor) ; Vošvrda, Miloslav (referee)
In this thesis, the aim is to employ some of the advanced probability and calculus techniques to financial mathematics. In the first chapter some major facts from continuous - time probability theory are presented. In the second chapter, one - dimensional stochastic diferential equations are introduced, we touch upon the questions of existence and uniqueness of solutions in full generality, construct a weak solution to the Engelbert - Schmidt equation and thoroughly present a known procedure called a Feller's test for explosions. In chapter three, focus is directed to a brief presentation of the well known Dirichlet problem. The problem is also interpreted financially, applied to options valuation and related approximations are implemented. The fourth, final, chapter concentrates on the Cox - Ingersoll - Ross model. Techniques derived in the second and third chapters are employed to thoroughly study the model properties.
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Modelování očekávané ztráty
Marada, Tomáš ; Lachout, Petr (referee) ; Franěk, Petr (advisor)
In this work we describe common credit risk models including all necessary mathematical theory. We extensively study Markov chains, especially homogeneous continuous-time Markov chains. The main contribution of the thesis is an extension of Markov chain modeling into stochastic time - so called time change. This extension allows us to capture better the system dynamics and introduce inhomogeneity into the model in a very elegant way. For practical modeling we derive many parameter estimators under different approaches to the time modeling. Further, we demonstrate the performance of these estimators on real data and simulation. At the end of the thesis we suggest some directions for further research.
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Simulation methods and risk management
Šemnická, Eliška ; Kuncová, Martina (advisor) ; Borovička, Adam (referee)
Project management is a field in which risk management can be applied. There must be a business case for any project to recognize its benefits for the company. A business case generally uses point estimation of input parameters and evaluates financial criteria for individual variants such as the net present value, pay-back period or internal rate of return. A simulation enables to design a model for the business case analysis while making use of the probability distribution. The model then turns from a deterministic into a stochastic one. The Monte Carlo simulation method, calculating a large number of variants, is employed in projects. The simulation can identify major risk factors, assess their probability and the significance of the impact on the evaluated financial criterion. The analysis outputs suggested by the simulation are the fundamentals of proper risk management. The Crystal Ball simulation software was employed for the calculation in this thesis.
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Option pricing under stochastic volatility
Khmelevskiy, Vadim ; Fičura, Milan (advisor) ; Janda, Karel (referee)
This master's thesis focuses on the problem area of option pricing under stochastic volatility. The theoretical part includes terms that are essential for understanding the problem area of option pricing and explains particular models for both option pricing under stochastic volatility and those under constant volatility. The application of described models is performed in the practical part of the thesis. After that particular models are compared to the real data.
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Models of time structures of interest rates and their use in valuation of liabilities of life insurance Company
Turussova, Valeriya ; Witzany, Jiří (advisor) ; Mazáček, David (referee)
This master thesis aims to describe problematics of the stochastic modeling of time structures of interest rates with Vasicek, CIR and Hull-White models and the use of these models in valuation of liabilities and time value of options and guaranties in life insurance. In the theoretical part of the thesis there are fundamentals of stochastic calculus, stochastic models of interest rates and introduction to problematics of life insurance defined. Furthermore, the last practical part of the thesis demonstrates impact of particular models on the value of liabilities in relation to clients and on the value of TVOG of real European life insurance Company.
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The stochastical approaches to the claims reserving
Hronová, Lucie ; Witzany, Jiří (advisor) ; Kolman, Marek (referee)
The subject matter of this master thesis is the introduction to the claims reserving methodology applied in the general insurance with the focus on the agragated data represented in the form of triangle schemes. First the basic deterministic methods are to be presented including the Chain ladder method as the most known and widely used tool in claims reserving. Next we will concentrate on the stochastic approaches. The method of bootstrapping is to be described more in detail as it is the main topic of this thesis. Finally the accuracy of the prediction of several specific models and algorithms is to be examined with the goal of their overall comparison (using randomly generated input data).
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Recent Trends in the Housing Market
Tsharakyan, Ashot ; Zemčík, Petr (advisor) ; Laurin, Frédéric (referee) ; Gilbert, Scott (referee)
In my dissertation I focus on exploring the major aspects of real estate markets' development over the last fifteen years. The dissertation includes theoreticalas well as empirical analysis of US and Czech real estate marketand consists of 4 chapters. In the first chapter the aggregate welfare effects of housing price appreciation in the presence of binding constraints are analyzed. The additional beneficial effect of housing price appreciation in the form of relaxation of credit constraints and opportunity for better consumption smoothing is taken into account when calculating the welfare effects of housing price appreciation. The effects of housing price appreciation are analyzed using both a model with exogenous housing prices based on previous literature as well as a newly developed model with endogenous housing prices. The second chapter explores theaggregate welfare effects of housing price changes in a stochastic general equilibrium framework with heterogeneous agents. The household sector in this model consists of two types of households, namely credit constrained and unconstrained ones, which differ both with respect to their time preferences as well as the structure of assets they own. The model also includes multi-sector production side and several sources of exogenous stochastic shocks....
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