Preprint - "Black Scholes Model - A Mathematical Method to Accurately Price Options"

Abstract: This paper will derive the Black-Scholes pricing model of a European option in two ways. We will assume that the price of a stock is log-normally distributed and derive the value of an option with expected value. We will also make use of Ito’s Lemma to justify the assumptions made in our first proof. In addition to this, we will prove put-call parity to price European put options. Finally, we will extend the original model developed by Black and Scholes to value options with unique characteristics, such as options in perpetuity and options encompassing two different types of dividends. The inspiration to personally conduct research and to derive the value of these sporadic options stemmed from the fact that they are always overlooked in other papers, despite their significance in specific scenarios.

Comments: 15 Pages, to be published in the Rocky Mountain Journal of Mathematics

2020 Mathematics Subject Classification. Primary: 60G44, 60H30; Secondary: 91B28, 91B70.

Key words and phrases. Black-Scholes Model, Real Options Valuation, Financial Derivatives, Quantitative Finance.