We are independent & ad-supported. We may earn a commission for purchases made through our links.
Advertiser Disclosure
Our website is an independent, advertising-supported platform. We provide our content free of charge to our readers, and to keep it that way, we rely on revenue generated through advertisements and affiliate partnerships. This means that when you click on certain links on our site and make a purchase, we may earn a commission. Learn more.
How We Make Money
We sustain our operations through affiliate commissions and advertising. If you click on an affiliate link and make a purchase, we may receive a commission from the merchant at no additional cost to you. We also display advertisements on our website, which help generate revenue to support our work and keep our content free for readers. Our editorial team operates independently of our advertising and affiliate partnerships to ensure that our content remains unbiased and focused on providing you with the best information and recommendations based on thorough research and honest evaluations. To remain transparent, we’ve provided a list of our current affiliate partners here.
Finance

Our Promise to you

Founded in 2002, our company has been a trusted resource for readers seeking informative and engaging content. Our dedication to quality remains unwavering—and will never change. We follow a strict editorial policy, ensuring that our content is authored by highly qualified professionals and edited by subject matter experts. This guarantees that everything we publish is objective, accurate, and trustworthy.

Over the years, we've refined our approach to cover a wide range of topics, providing readers with reliable and practical advice to enhance their knowledge and skills. That's why millions of readers turn to us each year. Join us in celebrating the joy of learning, guided by standards you can trust.

What is the Black-Scholes Model?

By Damir Wallener
Updated: May 17, 2024
Views: 12,052
Share

Options are a financial instrument giving the holder the right to buy or sell an underlying stock or commodity at a future point in time, at an agreed upon price. The Black-Scholes model, for which Fischer Black, Myron Scholes and Robert Merton were awarded the Nobel Prize in Economics, is a tool for pricing equity options. Prior to its development there was no standard way to price options; in a very real sense, the Black-Scholes model marks the beginning of the modern era of financial derivatives.

There are several assumptions underlying the Black-Scholes model. The most significant is that volatility, a measure of how much a stock can be expected to move in the near-term, is a constant over time. The Black-Scholes model also assumes stocks move in a manner referred to as a random walk; at any given moment, they are as likely to move up as they are to move down. By combining these assumptions with the idea that the cost of an option should provide no immediate gain to either seller or buyer, a set of equations can be formulated to calculate the price of any option.

The Black-Scholes model takes as input current prices, length of time until the option expires worthless, an estimate of future volatility known as implied volatility, and the so-called risk free rate of return, generally defined as the interest rate of short term US treasury notes. The model also works in reverse: instead of calculating a price, an implied volatility for a given price can be calculated.

Options traders often refer to "the greeks", especially Delta, Vega, and Theta. These are mathematical characteristics of the Black-Scholes model named after the greek letters used to represent them in equations. Delta measures how much an option price will move relative to the underlying, Vega is the sensitivity of the option price to changes in implied volatility, and Theta is the expected change in option price due to the passage of time.

There are known problems with the Black-Scholes model; markets often move in ways not consistent with the random walk hypothesis, and volatility is not, in fact, constant. A Black-Scholes variant known as ARCH, Autoregressive Conditional Heteroskedasticity, was developed to deal with these limitations. The key adjustment is the replacement of constant volatility with stochastic, or random, volatility. After ARCH came an explosion of different models; GARCH, E-GARCH, N-GARCH, H-GARCH, etc, all incorporating ever more complex models of volatility. In everyday practice, however, the classic Black-Scholes model remains dominant with options traders.

Share
WiseGeek is dedicated to providing accurate and trustworthy information. We carefully select reputable sources and employ a rigorous fact-checking process to maintain the highest standards. To learn more about our commitment to accuracy, read our editorial process.

Editors' Picks

Discussion Comments
Share
https://www.wisegeek.net/what-is-the-black-scholes-model.htm
Copy this link
WiseGeek, in your inbox

Our latest articles, guides, and more, delivered daily.

WiseGeek, in your inbox

Our latest articles, guides, and more, delivered daily.