Throughout the ECE Lab section we have learnt many electronics concepts and applied almost all of them directly or indirectly in our final lab project. Additionally, having taken away a lot from this course, we aimed to make a project that would challenge us academically and intellectually; for our final lab assignment, we made an autonomous line-following robot, that would follow a white line track using RedBot sensors, and would respond to audio cues from the environment using a microphone. In this report, we explain the use of each of the components that were used to make the final vehicle and the working of the vehicle itself.
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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.