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Options Valuation: The Discrete case
Šiklová, Renata ; Zahradník, Petr (advisor) ; Dostál, Petr (referee)
In this work we will get familiarized with a discrete valuation of options. A power- ful and widely applicable numerical method known as the binomial model will be established. Starting with a basic economic idea of non-arbitrage principle we build a risk-neutral world and develop the binomial model for call options. The general binomial model is extended into a trinomial model and there are several parame- terizations that are actually used in practice, provided for both of them. Great emphasis is also focused on a theoretical background. The theoretical knowledge, that will be introduced here in the discrete world, one can regard as basis for con- tinues models. The consequences of probability theory and risk-neutral valuation appear in the valuation of American options. There are three ultimate goals of this work: construction of the model itself, its implementation and an overview of the theoretical background. 1
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Interest Rate Models - Practical Aspects
Hakala, Michal ; Janeček, Martin (advisor) ; Sitař, Milan (referee)
Topic of the master thesis is practice of interest rate models. Literature dedicated to the interest rate models usually presents theory in very general form. Theory presented in general form leads to a gap between theory and practice. Author tries to fill this gap. Thesis describes basic theory and presents practical computations, which are relevant to generating interest rate scenarios. Contribution is given by derivation of formulas and computational methods in form directly applicable for implementation of presented models. It is common practice to validate quality of interest rate scenarios. Author presents several tests and implements them in programming language Python. Tests are implemented as application with graphical user interface.
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Využití nestandardních metod pro oceňování finančních derivátů
Švarcbach, Jan ; Witzany, Jiří (advisor) ; Maslowski, Bohdan (referee)
In this thesis we use nonstandard methods for the valuation of derivatives on electricity. We model the dynamics of electricity spot price as mean reverting processes on the hyperfinite binomial tree and by switching to the risk-neutral world we derive analytical formulas for the price of forward contracts. Both of our models are fitted to the German electricity market and forward price predictions are compared with forward products traded on the exchange. We conclude that both the Ornstein-Uhlenbeck and the Schwartz one factor model fit long-term forward contracts well while our prediction results for short-term forward prod- ucts are not conclusive due to low liquidity and alternative approaches might be suitable. 1
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Options Valuation: The Discrete case
Šiklová, Renata ; Zahradník, Petr (advisor) ; Dostál, Petr (referee)
In this work we will get familiarized with a discrete valuation of options. A power- ful and widely applicable numerical method known as the binomial model will be established. Starting with a basic economic idea of non-arbitrage principle we build a risk-neutral world and develop the binomial model for call options. The general binomial model is extended into a trinomial model and there are several parame- terizations that are actually used in practice, provided for both of them. Great emphasis is also focused on a theoretical background. The theoretical knowledge, that will be introduced here in the discrete world, one can regard as basis for con- tinues models. The consequences of probability theory and risk-neutral valuation appear in the valuation of American options. There are three ultimate goals of this work: construction of the model itself, its implementation and an overview of the theoretical background. 1
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