Glossário

# Black-Scholes Model

Easy

In simple terms, it is a mathematical formula that gives the fair price of stock options, allowing investors to calculate whether they are overvalued or undervalued.

## What Is the Black-Scholes Model?

In simple terms, it is a mathematical formula that gives the fair price of stock options, allowing investors to calculate whether they are overvalued or undervalued. But how did this formula come about and why has it stood the test of time on Wall Street?

Back in the 1970s, three professors—Fischer Black, Myron Scholes and Robert Merton—came together to solve a puzzle that had confounded Wall Street for years: how to accurately price stock options. They realized that there must be an efficient model to figure out the intrinsic value of these contracts.

After two long years filled with dead ends, eureka moments and scribbles on blackboards, their pioneering work resulted in the now renowned Black-Scholes model. What the professors achieved was no small feat. This formula would go on to transform how modern markets operate and even scored Merton and Scholes the 1997 Nobel Prize in Economics. Black had unfortunately passed by then, making him ineligible for the prize.

## What Are the Formula’s Components?

The Black-Scholes model is essentially an equation for calculating the theoretic price of stock options. The brilliant trio's major breakthrough was considering the changing price of the underlying asset over time. Their formula incorporated five key variables:

• The current stock price

• The strike price of the option

• The expiration time of the contract

• The volatility of the underlying stock

• The prevailing risk-free interest rate

The formula looks something like this:

By inputting these elements into the model, one could determine whether an option was fairly valued. It also allowed traders to assess the likelihood of that contract expiring “in-the-money”—financial jargon for being profitable.

## Why Was It a Gamechanger for Wall Street?

Picture Wall Street as a marketplace in the pre-Black-Scholes era. Nobody knew how to systematically estimate options prices. Most market players relied on past experience or basic calculations when trading these contracts. The Black-Scholes-Merton model changed all that by offering two major advantages:

1. It gave traders a benchmark for whether options were mispriced in the market. Savvy investors could scoop up undervalued contracts or sell overvalued ones for easy profits.

2. The formula also lets traders better hedge risks and optimize their portfolios around options positions. By enabling accurate valuation and risk management for options, the model brought greater efficiency and transparency into capital markets—that’s a win for all participants!

## Does It Have Any Shortcomings?

While game-changing, the Black-Scholes model makes some simplifying assumptions:

• It assumes constant volatility of the underlying stock. But in reality, volatility fluctuates all the time!

• It assumes risk-free interest rates stay flat. However, interest rates can change depending on different economic factors.

• It discounts the possibility of early exercise for American options. Most options traded in the U.S. can actually be exercised by buyers before expiration.

As academic understanding of options advanced, newer pricing models have emerged to complement Black-Scholes. But the underlying principles and intuition remain relevant today. Almost 50 years on, Black-Scholes still features heavily in most options trading platforms and calculators.

## Have Regular Investors Benefitted From This Model?

While the average investor may feel disconnected from academic financial theories, the Black-Scholes model has undoubtedly influenced how markets operate. For starters, it made options far easier to grasp for everyday traders by enabling exchanges to systematically quote prices.

Access to models like Black-Scholes has also allowed retail investors and small firms to participate in a market once dominated by institutions. So arguably, these pioneering professors have left all of us better off.