Derivation of Black-Scholes Equation Using Itô's Lemma

Abstract

The Black-Scholes Equation is arguably the most influential financial equation, as it is an effective example of how to eliminate risk from a financial portfolio by using a hedged position. Hedged positions are used by many firms, mutual funds and finance companies to increase the value of financial assets over time. The derivation of the Black-Scholes equation is often considered difficult to understand and overly complicated, when in reality most confusion arises from misunderstandings in notation or lack of intuition around the mathematical processes involved. This paper aims to take a simple look at the derivation of the Black-Scholes equation as well as the reasoning behind it.