Partial differential equations in finance : The case of The American Option

Abstract

This work introduces the well known Black-Scholes partial differential equation. Namely,the focus is on its application on assessing the value of American options. This is an important topic in finance, as researchers are still looking for time efficient methods tovalue certain types of options. Three different numerical methods will be explained and studied: the explicit method, the operator splitting method, as well a the penalty method. A case study was also carried out in order to motivate the importance of knowing the value of our options. Having a solid understanding of the mathematics behind stock options and the way they fluctuate is essential to prevent ourselves from financial losses.