The Equation That Changed Wall Street: Understanding Black–Scholes
Intro The Black-Scholes Equation is one of the most valuable and impactful advanced financial models in Wall Street history. In this article, I will discuss what it is, how markets and institutions use it, and why it is essential. What is it? The Black-Scholes financial model/equation, denoted through the equation above, is a mathematical formula used to calculate the fair price of options for equities, where an option is a contract that lets you buy or sell a stock at a set price in the future). In a financial system where volatility is widespread and inevitable in all sectors, based on a geometric Brownian motion (signifies natural volatility in markets), the Black-Scholes model hedges option with underlying assets, leading to a risk-neutral valuation (removes risk) for options. Fischer Black and Myron Scholes included four different groups of terms, Volatility (randomness of price), Delta & Gamma (sensitivity to price changes), Theta term (time decay), and Risk-free (discounting...