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.
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