Modelos estocásticos de precios y valoración de opciones

Abstract

[en] Since the creation in 1973 of the first stock Exchange exclusively dedicated to financial options, and the irruption of Mathematics in this discipline, leaded by Fisher Black and Myron Scholes, there have been numerous investors who have predicted the option’s price behavior backed by the principles of Black-Scholes model in order to perform safer investments. However, focusing on the current situation of Stock Market, where uncertainty prevails due to the sanitary crisis provoking huge variations in stock prices in short periods of time and the growing preference by investors in assets such as cryptocurrencies, highly volatile assets, the Black-Scholes model is found to be useless, forcing investors to use other models. The aim of this project is to perform an introduction to 1976 Robert C. Merton Jump-Diffusion model, introducing this way an alternative model to Black-Scholes one, which will take in account situations in which stock prices experiment significant variations in short periods of time, just as it occurs in nowadays market. It will be also introduced the 2002 Kou model, as an alternative Jump-Diffusion model to Merton’s in the particular case of dependent option pricing. It will finish with the statement and demonstrations of 2004 Kou-Wang theorem, which gives the investors a barrier options pricing formula.