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Publication . Bachelor thesis . 2022

Binomski in trinomski modeli za vrednotenje opcij

Mikola, Žan;
Open Access
Slovenian
Published: 26 Aug 2022
Country: Slovenia
Abstract
V delu diplomskega seminarja bom predstavil, kaj so evropske opcije in nekaj modelov za vrednotenje evropskih opcij, ki jih bom tudi primerjal. Zaradi kompleksnosti zahtevnejših modelov bom v delu opisal tudi nekaj pomembnejših konceptov, ki so potrebni za njihovo izpeljavo. Med te koncepte spadajo Markovski proces, Wienerjev proces, Itôv proces. Modele bom predstavil v treh kategorijah: binomski, trinomski in zvezni. Od binomskih modelov je najpomembnejši ravno osnovni Cox, Ross in Rubsteinov model za vrednotenje opcij z diskretnimi časi, iz katerega sledi izpeljava Black-Scholesovega modela, ki temelji na predpostavki o zveznosti. Glavni poudarek diplomskega dela bo predvsem na predstavitvi modela za vrednotenje opcij, ki sta ga izpeljala Bardia Kamrad in Peter Ritchken. To je trinomski model, ki se z relativno malo računanja hitro približa vrednostim po Black-Scholesovem modelu. Ta model bom primerjal tudi z osnovnim Cox, Ross in Rubsteinovim modelom in nato predstavil izrek, ki pravi, da je Kamrad-Ritchkenov trinomski model formalno ekvivalenten binomskemu, pod določenimi pogoji. In my thesis, I am going to present European options and a few models for their pricing. Presented models will be compared to each other. I will also introduce a few of the most important concepts which are necessary for the their derivation. These concepts are Markov process, Wiener process and Itô' s process. Models for option pricing will be presented in three groups: binomial models, trinomial models and continuous models. The simplest binomial model is Cox, Ross and Rubstein's model for options pricing. It is a discrete model from which we derive the continuous Black-Scholes model. The main part of the thesis is the trinomial model for option pricing which was developed by Bardia Kamrad and Peter Ritchken. This trinomial model computes the option price approximation relatively fast and with little computing. The price given by this model will be compared to prices computed by the Black-Scholes model (which should give true values). In the thesis, I will also state the theorem about binomial and trinomial models. The theorem says that the Kamrad-Ritchken trinomial model is formally equivalent to the binomial method, under some conditions.
Subjects by Vocabulary

Universal Decimal Classification: udc:519.8

Subjects

opcija, binomski model, trinomski model, option, binomial model, trinomial model

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