In this paper we discuss how to price American, European and Asian options using a geometric Brownian motion model for stock price. We investigate the analytic solution for Black-Scholes differential equation for European options and consider numerical methods for approximating the price of other types of options. These numerical methods include Monte Carlo, binomial trees, trinomial trees and finite difference methods. We conclude our discussion with an investigation of how these methods perform with respect to the changes in different Greeks. Further analysing how the value of a certain Greeks affect the price of a given option.
Original Draft by Joseph Timothy Foley (foley AT ru DOT IS) and by David S. Cochran (cochrand AT ipfw DOT edu)
Updated for ECE405 by Joseph Smith (smitjj09 AT students DOT ipfw DOT edu)
Cybersecurity MsC Template for University of Padua, adapted from official LaTeX template and Stefano Della Morte's Data Science template. It includes minor tweaks on the color and captions and fixes an error on the font size.