Option pricing models

What is the Black-Scholes Options Pricing model, and why is it wrong?

Option pricing history

To understand where we’re at today, we first have to travel back to 1973. Fischer Black and Myron Scholes had just published The Pricing of Options and Corporate Liabilities, and it was taking the options industry by storm.

Pricing assumptions

They had published an equation that claimed to price any European call option fairly, according to the following assumptions:

1. The movement of the underlying stock is random, normally distributed, and follows a pattern that resemble a random walk.
2. The option can only be exercised at expiration (otherwise known as a European option). Options that you see today when you log in to your broker are American options - they can be exercised at any time.
3. The volatility of the underlying stock is known and constant.
4. The risk-free rate is known and constant.
5. No dividends are paid out during the life of the option.

Navigating a changing environment

At the time, this was a groundbreaking formula. 24 years later, Black and Scholes would win the Nobel Prize for their work on this exact equation. It was used, and continues to be used, as the standard option pricing model in many copies of software around the world. However in recent years, its reliability and accuracy in determining the true value of an option has been called into question.

This is because in the real world of trading, the assumptions stated in the Black-Scholes model no longer hold true. In 1973, the options market was very illiquid, and it was only in that same year that the Chicago Board Options Exchange (CBOE) became the first U.S. exchange to offer listed stock options.

Since then, the popularity and accessibility of options trading has skyrocketed, and in turn, so has volatility, with GameStop recently reaching an unprecedented 1000% implied volatility. With volatility swinging between 10% and 1000% in a one-week span, it’s no wonder that assumption #3 has gone out the window.

A new set of assumptions

To say that an increase in volatility is the only reason the Black-Scholes model no longer works would be a dramatic oversimplification. There are several other factors that we will touch on throughout these lessons:

The recent availability of weekly and daily expirations

Before the 2010s, most listed options expired at the end of the month. That was just all that was offered - there simply wasn’t enough liquidity and volume in the market to trade at a higher frequency. The retail options trading boom over the last several years has set in motion a pattern for more and more listings. How soon will it be before we see hourly expirations?

A worldwide shift in how investors approach risk

Black Swan events, a term popularized by former options trader Nassim Nicholas Taleb in his book The Black Swan: The Impact of the Highly Improbable, are highly unlikely, unpredictable outlier events that can often lead to devastating losses. The housing crisis in 2007 and COVID-19 are both examples of Black Swan events.

Thus, the approach of using options to hedge your risk against these events has gained traction. This in turn has led to call and put options having different volatilities, a phenomenon we will cover in another lesson.

Increased trading around earnings dates

It is well documented today that implied volatility increases leading up to earnings, and then falls back sharply to normal levels after earnings are reported. The quick changes in implied volatility certainly don’t meet assumption #3 in the Black-Scholes model.

When Black and Scholes published their pricing model in 1973, they had no idea what the next several decades would hold. Now, 50 years later, we face a much different world, but the question remains: how do we determine the true price of an option?