Generalized Cox - Ross - Rubinstein Model

Ovaj diplomski rad objedinjuje istraživanja binomnih modela za nearbitražno vrednovanje europske opcije. Proučava se princip određivanja cijena financijskih imovina u općenitom modelu u diskretnom vremenu te izvodi eksplicitna formula za cijenu europske call opcije u binomnom modelu s n perioda. Pokazuje se da nije riječ o jedinstvenom modelu, već o familiji interpretacija procesa u diskretnom vremenu koji konvergira prema geometrijskom Brownovom gibanju. Očito je da bi preferirani binomni model trebao biti karakteriziran odsustvom arbitraže u konačnom broju vremenskih koraka i rezultirati točnom volatilnošću, no neki modeli ipak ne ispunjavaju ove zahtjeve. Izvodi se generalizirani binomni model, a dobiveni rezultati se ilustriraju i provjeravaju numeričkim primjerom.This paper synthesizes the research on binomial models for European options. The principle of pricing financial assets in a general model at discrete time is studied and an explicit formula for pricing European call option in a binomial model with n periods is derived. Paper shows that the model is not a single model but a family of interpretations of a discrete-time process that converges to the geometric Brownian motion process in the limit. It would seem that a preferable binomial model should prohibit arbitrage for a finite number of time steps and recover the correct volatility, and some models fail to meet these requirements. A generalized binomial model is derived and obtained results are illustrated and verified by a numerical example