Understanding Option Pricing: Calculations & Models | Ally (2024)

• Feb 13, 2023
• 8 min read

• What factors determine option pricing

• How option contract pricing works

• Important option pricing models

For many investors, it’s exciting to buy a stock on the cheap and rack up as many shares of that stock as possible. The stock option world is different, though. And it’s important to boost your understanding of options and option pricing to help make better trading decisions and reduce your chances of making common option trading mistakes .

Fortunately, if you understand how car insurance pricing works, then you’re well on your way tounderstanding option pricing.

Just like car insurance is based on the probability of a future event (like a rush-hour fender bender), option contracts are based on the probability of a future event — in this case, the rise or fall of a particular stock’s price over a defined period of time.

A quick look at the history of options as “insurance” offers a better understanding of current options pricing — and it all started with tulips.

The 16th-century Dutch tulip craze presented perhaps the first speculative market bubble in which investors sold land and other hard-valueassets to purchase exotic tulip bulbs at unbelievably high prices. Once prices reached all-time highs, investors started to “insure” their purchases with put options, giving them the right to sell their bulbs at a guaranteed price if the market dropped.

Like tulip speculators, today’s investors still use options for “insurance.” Put options can help protect long positions against a drop in the underlying’s price. Call options can offer similar protection for short sellers — but that’s a more advanced topic that we won’t explore here.

While supply and demand play a role in options prices, so do the underlying stock’s movements, time to expiration and several other factors. If the price of Stock XYZ rises by one dollar, options based on XYZ will probably move, too. But they might not move as much as options based on a different underlying stock — let’s call it Stock ABC. This is another way of sayingthat options prices aren’t strictly based on movement in the underlying stock price.

The five factors that determine car insurance prices are basically the same factors that drive options prices. Our car insurance comparison offers a great way to keep them straight.

Although people don’t often think of cost-of-carry when buying car insurance, it’s a pricing factor. When you purchase an insurance policy, for instance, you pay for the policy upfront — the insurance company earns interest on those fundsthroughout the life of the policy. The same concept holds for options. When you buy an option, you pay for it right away, so the seller can earn interest on your dollars.

There’s one twist in that metaphor: Dividends. Whereas car insurers don’t pay anything like dividends to car owners, stocks will sometimes pay a dividend to shareholders. Option pricing model calculations take potential dividends into account.

Now we come to that mysterious variable, risk. In the car-insurance world, actuaries rely on statistics and the driver’s profile to determine their risk of getting into an accident versus someone else’s. In the options marketplace, risk is measured in volatility. Volatility in options comes in two flavors: Implied volatility and historical volatility. For now, we’ll focus on the latter concept.

Historical volatility is defined in textbooks as “the annualized standard deviation of daily stock price movements.” Put in plain English, let’s just say it’s how much the stock price fluctuated on a day-to-day basis over a one-year period.

Even if a $100 stock winds up at exactly $100 one year from now, it still could have a great deal of historical volatility. After all, it’s possible that the stock could have traded as high as $175 or as low as $25 at some point. And, if there were wide daily price ranges throughout the year, it would indeed be considered a historically volatile stock. The more volatile a stock, the riskier, which means “insuring” it with options will be more costly.

To understand how option contract pricing works, we first need to look at the basics of option pricing models and the variables used to calculate the theoretical value of an option.

Let’s start with two key variables: Intrinsic value and time value.

Time value refers to the part of an option price based on its time to expiration. If you subtract the amount of intrinsic value from an option price, you’re left with the time value. If an option has no intrinsic value (say, it’s out-of-the-money), its entire worth is based on time value.

The intrinsic value is pretty straightforward: Simply look at where the underlying stock is relative to the strike price of the option contract. If your option’s strike price looks like a better deal compared to the current stock price, then your option is considered “in-the-money.” And the amount the option is in-the-money is that option’s intrinsic value. If it does not have any intrinsic value, then it’s only made up of extrinsic value or time value. In other words, an option is considered out-of-the-money when it has zero intrinsic value, only time value.

Now, figuring out the time value portion of an IN or OUT of the money option is a bit trickier. To calculate this, you’d need to take all the factors we mentioned above (stock pricing, strike pricing, expiration date, interest rates and dividends, volatility) and input these factors into an option pricing model to give us a starting point for the price of an option contract. The model is theoretical in nature, and there are always real market forces that will play into the price. But again, options are not priced like stocks. It’s important to gain a basic understanding of why an option is trading for that price in the marketplace. This knowledge will help you develop realisticexpectations of how your option price might react when conditions in the marketplace change.

Want to dig deeper? Here are some ways.

An option pricing model is a mathematical formula used to calculate an option’s theoretical value using its strike price, the underlying stock’s price, volatility and dividend amount, as well as time until expiration and risk-free interest rate.

If stats are your thing, read on for an overview of two prominent models and where you can learn more.

Two option pricing models worth knowing are the Black-Scholes and binomial models. A quick Internet search yields lots of information about them. To point you in the right direction, here’s a quick overview.

The Black-Scholes model is a mathematical model, devised in 1968 by economists Fischer Black and Myron Scholes. It values the expected return of a security, giving a theoretical estimate of the price of European-style options.

The binomial model, on the other hand, was developed in 1979 and values options using an iterative approach utilizing multiple time periods to value American options.

One more thing to note: Option pricing models typically generate something called the option Greeks: Delta, gamma, theta, vega and rho. So, it’s a good idea to take time tomeet the option Greeks.

Option contracts are based on the probability that something is going to happen in the future — like the rise or fall of a particular stock’s price. But, as we established, the underlying stock’s price movement is only one factor in determining an option’s price. Understanding basic concepts about option pricing could improve your ability to make trade decisions and your application of option trading strategies.

In essence, understanding option pricing theory moves you beyond the world of an option trading novice and positions you to make more informed investment decisions.