Αποτίμηση δικαιωμάτων προαίρεσης με τεκμαρτό τριωνυμικό δέντρο

Abstract

This thesis presents an options valuation lattice model through the construction of an implied trinomial tree. The main purpose is to construct a model in which the information provided by implied volatility will be integrated making it more accurate for the valuation of options. Firstly, we present a brief historical review towards the need to find a more efficient option pricing model, secondly we analyze the problems that arise by using constant volatility in pre-existing models. We proceed with the theoretical analysis of the models starting from the binomial valuation model, continuing with the trinomial tree model as a two step binomial, and reaching at the main topic, the construction of an implied trinomial tree for the valuation of European call and put options. Based on the theoretical analysis, the appropriate algorithms are created in order to conduct the empirical study. For a sample of historical days, the available call and put options are collected, the implied volatility is estimated and finally, the implied trinomial tree is constructed. After valuing the sample options via the above models, we conclude that the implied trinomial tree model is more flexible and effective for valuing European call and put options. Also, it can be extended to the valuation of American type options since it refers to discrete time.