Valoració i cobertura d’opcions financeres utilitzant EDPs i diferències finites

Abstract

[en] Introducing ourselves in the world of finance, we propose final boundary value problems that arise when pricing and hedging certain financial derivatives, specifically plain vanilla european options and some exotics such as Asian, lookback and barrier. Due to its important influence on the current way of pricing and hedging financial options, we will assume the Black-Scholes model. There are closed formulas for the simplest financial options but, unfortunately, not for the vast majority of them. Even when there exist explicit solutions, these are very complex and they are lacking of utility in practice. These factors often make us resort to numerical methods. Using the finite difference method, we will obtain approximate solutions to the posed problems and we will verify the efficiency of the numerical solutions that it offers us.