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Interest Rate Models
Butkovičová, Ivana ; Popela, Pavel (referee) ; Chvátalová, Zuzana (advisor)
This bachelor’s thesis focuses on a description of the interest rate models that are applied in the sphere of financial mathematics. Furthermore, it specifically describes the Vašíček model, Cox-Ingersoll-Ross model, Ho-Lee model and Hull-White model. These models are given by the stochastic differential equations. The main terms of the Stochastic Calculus are described in the theoretical part of the thesis. All the above models are also calibrated. Moreover, the spot and forward interbank interest rate—LIBOR is described in the thesis. By applying specific data, that are available in the public database of the Czech National Bank, we have simulated the Vašíček and Cox-Ingersoll-Ross models. The obtained results are interpreted.
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Interest rate options and their valuation in binomial model
Ondruš, Martin ; Slámová, Lenka (advisor) ; Hurt, Jan (referee)
This work discusses about binomial pricing model, which is the basic principle for pricing of any kind of financial assets. We define its brief definition and show its main characteristics. Next, this work discusses about models of the short rate, especially to their discrete versions. From this set of models, we choose one of the most important interest rate models, which is Ho-Lee model and we look at it in details. According to its basis we interpret calibrating of binomial tree. Finally, we perform how to price different kinds of interest rate options such as caps or barrier options according to Ho-Lee model as well. We use mathematical software Mathematica for pricing options and calibrating of binomial tree.
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Interest Rate Models
Butkovičová, Ivana ; Popela, Pavel (referee) ; Chvátalová, Zuzana (advisor)
This bachelor’s thesis focuses on a description of the interest rate models that are applied in the sphere of financial mathematics. Furthermore, it specifically describes the Vašíček model, Cox-Ingersoll-Ross model, Ho-Lee model and Hull-White model. These models are given by the stochastic differential equations. The main terms of the Stochastic Calculus are described in the theoretical part of the thesis. All the above models are also calibrated. Moreover, the spot and forward interbank interest rate—LIBOR is described in the thesis. By applying specific data, that are available in the public database of the Czech National Bank, we have simulated the Vašíček and Cox-Ingersoll-Ross models. The obtained results are interpreted.
|
|
|
Interest rate options and their valuation in binomial model
Ondruš, Martin ; Slámová, Lenka (advisor) ; Hurt, Jan (referee)
This work discusses about binomial pricing model, which is the basic principle for pricing of any kind of financial assets. We define its brief definition and show its main characteristics. Next, this work discusses about models of the short rate, especially to their discrete versions. From this set of models, we choose one of the most important interest rate models, which is Ho-Lee model and we look at it in details. According to its basis we interpret calibrating of binomial tree. Finally, we perform how to price different kinds of interest rate options such as caps or barrier options according to Ho-Lee model as well. We use mathematical software Mathematica for pricing options and calibrating of binomial tree.
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