Stochastic volatility models

Abstract

Treball de Fi de Grau en Economia. Curs 2020-2021

Tutora: Elisa Alòs

The Black Scholes formula is one of the most used to determine what is the fair value of options. However, there are some assumptions such as that volatility is constant that are not met in the real market. Stochastic volatility models can be used as an extension of Black Scholes where volatility is a random process. The aim of this project is to use the SABR model which is a stochastic volatility model to attempt to capture the volatility smile. We study classical problems related to the SABR model such as simulation. Finally, we study its implementation by the financial industry and its main limitations.