**How Are Options Values Calculated? Learn the Methods Here**

In many ways, options are just like any other investment. Investors need to understand what determines their price before delving into the practice of trading these contracts.

When buying or selling bonds, commodities, or stocks, the trader must try to predict whether or not the asset will end up profitable. This article explores option value calculation, so novice investors can learn how to take advantage of stock movements and improve their financial positions.

**Key points of this article:**

- Options are derivative contracts that give the holder the right, but not the obligation, to buy an asset at a predetermined strike price before it expires.
- An option’s price is primarily made up of its intrinsic value and time value.
- The intrinsic value of an option is the amount by which its strike price is ‘in the money’ as compared to its market price.
- Time value is based on the option’s expected volatility and how much time is left before the asset’s contract expires.
- Volatility can be a double-edged sword. It provides investors with the potential for significant returns, or it can lead to sizable losses.
- Options contracts are typically priced using mathematical formulas like the Black-Scholes, Binomial, and Trinomial models.

## Options Pricing Factors

Image via Flickr by kenteegardin

Before venturing into the world of trading options, investors should have a good understanding of all the components that go into determining an option’s value. These include:

- Time to expiration (a.k.a. time value).
- Underlying price.
- Strike price.
- The intrinsic value.
- Volatility.
- Interest rates.
- Cash dividends paid.

## Market and Strike Price

The value of calls and puts are affected by changes in the stock’s market price. It’s a relatively straightforward concept. When the stock price goes up, calls should gain in value. Likewise, calls should drop as the stock price falls.

An option’s strike (or exercise) price is a predetermined amount at which an investor can buy or sell an asset. If the strike price is above the underlying market price, the option is considered profitable.

## Intrinsic Value

The intrinsic value would measure an option’s profitability based on its strike price versus its market price — if the option were exercised today. If the option’s strike price is not profitable compared to the stock price, the asset is said to be out of the money. On the other hand, it’s considered in the money if the stock option’s strike price is equal to or greater than its market price.

Although intrinsic value includes the relationship between the strike price and the stock’s price in the market, it doesn’t account for the passage of time. The expiry (how much time is remaining until the option’s expiration) significantly impacts an option’s premium or value.

## Time Value

Since options contracts have a finite amount of time before they expire, that remaining amount of time has a monetary value. This is an important concept for securities investors to grasp. The more time an option has until it expires, the greater the chance its intrinsic value will end up in the money. It’s essentially the value of the premium after calculating the profitability between the strike price and the asset’s market price.

The time component of an option decays exponentially. Typically an asset can lose up to a third of its value during the first half of its life and two-thirds during the second half. An option’s time value is also dependent on the volatility the market expects the stock to display up to expiration. Its premium may expire higher as a result of the increased probability that the stock’s price could exceed its strike price. For stocks that aren’t expected to move much, the option’s time value stays relatively low.

## Volatility

The term volatility in option value calculation represents how large an asset’s price swings around the mean price. Essentially, it’s a statistical measure of its range of potential outcomes based on the historical performance of its returns. This roughly equates to the option’s level of uncertainty or risk, as its value can be spread out over a large range and can change dramatically — in either direction — in a short period of time.

Beta is one of the metrics used to measure a stock’s volatility compared to the overall market. Most options with high volatility have a better chance of expiring in the money due in part to the uncertainty of the stock’s market price before the option expires. Just keep in mind, however, that high beta stocks also come with more risk.

The effect of volatility is difficult to quantify as it’s mostly subjective. Fortunately, there are several online calculators to help investors estimate volatility.

To make the matter even more interesting, there are several types of volatility, including the most noteworthy: implied and historical.

### Historical Volatility

Historical volatility helps traders determine the possible magnitude of the option’s future moves. It’s based on real-world data and is expressed as a percentage. By looking back and measuring a stock’s price changes over time, one can see how volatile the option’s market has been. This helps novice options investors develop a strategy to choose which exercise price is most appropriate for a particular option.

### Implied Volatility

Implied volatility is used with theoretical models. It refers to the stock’s projected volatility and is one of the most important metrics for options traders because it helps set the current price of an existing option. Investors also use implied volatility to assess the potential profits of a trade.

This model measures what an option’s future volatility may be and is a reflection of the market’s current sentiment. This method varies from historical volatility, which relies on past performance. However, it’s often considered a more prevailing metric as it looks forward, not backward.

## Option Value Calculation Models

There are several commonly used option pricing models in place today. These mathematical principles use certain parameters to calculate the theoretical fair market value of an option. Here are three of the most popular systems:

### The Black-Scholes Formula

The Black-Scholes model is the most widely known way to calculate option pricing. The math involved in this formula’s differential equation can be complicated and intimidating for both new and veteran options traders alike. When applied to a stock option, the Black-Scholes model incorporates these variables:

- Constant price variation of the stock.
- The option’s strike price.
- Time value of money.
- Time to the option’s expiration date.

Fortunately, investors don’t need to know or even understand the math to use Black-Scholes modeling in their strategies. There are a variety of online options calculators and robust analysis tools used by many of today’s trading platforms that output the options pricing values quickly and painlessly.

### Binomial Options Pricing Model

The binomial option pricing model was developed in 1979 and uses a procedure that allows for the specification of multiple periods during the time span between the valuation date and the option’s expiration date.

With this intuitive approach, there are two possible outcomes that follow a binomial tree: a move up in value or a move down. The major advantage of a binomial option pricing model is that it’s mathematically simple compared to other methods, which is why this formula is becoming more commonly used in today’s marketplace than the well-known Black-Scholes model.

### The Trinomial Tree

Developed by Phelim Boyle in 1986, the trinomial tree model is a lattice-based computational that is conceptually similar to the binomial options pricing model. This theory incorporates three possible values that an underlying asset can have in one time period: greater than, the same as, or less than its current value. The Trinomial equation is more accurate than the binomial method and computes the same results in fewer steps. However, it never gained the popularity of the other models and is rarely used at this point.

## The Bottom Line

O ption pricing theory uses a variety of complex variables to theoretically value an option. The primary goal of option value calculation is to determine the probability that an asset will expire in the money. This guide aims to give investors a better understanding of how option value calculation works, so they can potentially improve their portfolio.