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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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Pricing with interest rate trees
Novotová, Simona ; Starinská, Katarína (advisor) ; Branda, Martin (referee)
This thesis deals with interest rate trees, their construction and use in pricing. At the beginning, work deals with various types of interest and selected financial derivatives, which need to be properly priced. For pricing, it is necessary to know the evolution of interest rates, which is simulated by various stochastic models. Next section offers summary of the models. For two models (Rendelman-Barter and Hull-White model) the construction of a binomial and trinomial tree is studied. The work describes a two-phase algorithm, which is used for generation of trinomial tree. Interest rates obtained from the constructed tree are used for the valuation of bond options.
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Valuation of Structured Products
Dohnálek, Jan ; Brada, Jaroslav (advisor) ; Kováč, Michal (referee)
The objective of the thesis is to acquaint readers with field of structured product valuation. It is a relatively complex issue which is, however, based on general valuation foundations. The opening chapter is dedicated to these general fundamentals of valuation. Emphasis is placed mainly on present value principle, a specific variant of comparison, and its related aspects. The second section describes key elements of structured product valuation. Greater part of this chapter is devoted to the Monte Carlo simulation, the most employed tool in valuation of these products in practice. An important part of Monte Carlo simulation is an option spread, which arises as by-product of the simulation and reflects value of an option contained in the evaluated instrument. Third chapter is focused on interest rate and prepayment models. Level of prepayment is dependent on interest rates development which both are the most critical factors that affect value of structured products. Description of models includes theoretical and mathematical formulation as well as mentioning their advantages and disadvantages. Valuation model is illustrated in the last part, which is demonstrated on valuation of hypothetical structured products example. Based on the model, the development of cash flows from underlying asset portfolio is forecasted which in turn determines the value of evaluated instruments. The final section deals with advantages of structured products and, hence, why banks and other institutions use them in practice.
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