Options contracts are some of the most powerful financial instruments available to traders. However, options are also complex. Therefore anyone who trades options seriously should be able to answer one of the most fundamental options questions: from where do options get their value?

The price of an option, also referred to as the “option premium”, is the price the buyer pays to the contract “writer”. Options traders typically rely on a formula called “Black-Scholes” or “Black-Scholes-Merton” to calculate their value. This formula was created in 1973 by three Nobel prize-winning economists.

To this day, the equation remains the most widely accepted formula in options pricing because it easily allows traders to input discoverable data points of an underlying security and its option contract as a means of arriving at a fair value.

It should be mentioned that although the Black-Scholes-Merton equation is quite useful, it fails to account for some variables that have a material effect on the option’s price, such as dividend payouts issued by the underlying security over the life of the options contract.

The equation does, however, take into account most of the key drivers of an option’s value. The equation to price a call option contract per the Black-Scholes-Merton method appears below.

While this equation may seem complicated, you don’t need to feel intimidated. It’s more important to understand the overall theory of two of the key components expressed here – extrinsic and intrinsic value – than it is to understand the math behind the formula.

The extrinsic value of an option is what traders sometimes call its “time value”. This is the component of the option that represents the value of all the possible paths that the underlying security could take between now and the expiration date. The extrinsic value is calculated by subtracting the intrinsic value, which will be discussed in the following section, from the total option price.

Another way to think about the extrinsic value of the option is that it represents the value of uncertainty.

Uncertainty offers value to both the buyer and seller of an option because it represents the potential for an option to settle in or out of the money. The greater the uncertainty, the higher the potential for either scenario to transpire.

To account for this uncertainty, the Black-Scholes-Merton formula fits a probability distribution around two key parameters of the underlying security. We will discuss this calculation in greater detail later.

The intrinsic value of the option, also known as the “parity value”, is the difference between the current price of the underlying security and the strike price of the option contract. The wrinkle, however, is that the minimum intrinsic value can never fall below zero.

It’s far easier to calculate the intrinsic value of a call option., Simply take the current price of the underlying security and subtract the strike price of the option. To calculate the intrinsic value of a put option, take the strike price and subtract the underlying security’s current price. Intrinsic value is therefore a function of a single parameter:the difference between the underlying security’s current price and the option’s strike price.

Now that we have covered the topics of extrinsic value and intrinsic value,, let’s dive a bit deeper into three key differences between them.

The intrinsic value of an option is a function of the underlying security’s current price relative to the option’s strike price. Extrinsic value on the other hand is derived independently of those two variables. Instead, extrinsic value is dependent on the implied volatility of the underlying security and the time-to-expiration of the option contract.

Implied volatility is the rate at which the market believes the price of a security will increase or decrease over a particular period of time in the future. It is often calculated with standard deviation as an input, and may at times be expressed through measurements such as “variance” and “beta”.

The Black-Scholes-Merton equation uses Standard deviation in its formula.as a proxy for the uncertainty surrounding where the price of the underlying will settle at the time of expiration.

Recall that extrinsic value refers to the component of the option pricing formula that represents the value of that uncertainty, or in other words, the path of price action that a security might experience between now and expiration. Also recall that intrinsic value functions independently of the implied volatility of the underlying security. The greater the implied volatility of a security, the greater the number of “paths” its price may take towards it settlement on expiration.

Moreover, a trader should be willing to pay more for an option contract whose underlying exhibits greater implied volatility because the price movement indicates that there is a greater chance that the security will settle above the strike price for a call or below the strike price for a put, at the time of expiration. The implied volatility component is comparable to the time component, which we will describe below, in terms of its influence on elements of the extrinsic value of an options contract..

The time component is the part of an option’s extrinsic value that represents the decaying value between the current day and the expiration date. It’s typically calculated using trading days as units. The impact of the time component functions the same across options types, meaning there is no difference in influence depending on whether the instrument is a call or put. All things being equal, the value of an option naturally decreases as the number of days-to-expiration gets smaller. Intuitively, this positive relationship between time-to-expiration and the value of the options contract makes sense. It relies on the same logic that we used when determining the value of the volatility component earlier:. The greater the number of days to expiration, the greater the number of paths that the price of the underlying security can take between now and the day of expiration. Together with the volatility component, the time component of an option contract make up the total extrinsic value of an option. Intrinsic value on the other hand, had no relationship to the amount of time that remains on an options contract before it expires.

To better illustrate how the concepts of intrinsic and extrinsic value relate to the aggregate price of an options contract, we use a few a real-world examples of options on Tesla and Apple stock.

Tesla Inc (TSLA) is a security that currently exhibits an implied volatility of 34% for the 3/18/2022 option expiry.. Implied volatility is simply a measure of the expected annualized volatility of the underlying security that options traders are pricing into the option and is calculated by solving the Black-Scholes-Merton equation for the volatility term. AAPL’s implied volatility for the 3/18/2022 expiry is 24% which would indicate that options traders are expecting AAPL to exhibit lower volatility than TSLA over the period ended on the expiration date. Later on, we’ll see how this stark difference in implied volatility is what is called the “volatility component” of options, resulting in a material difference in the price of options for these two companies.

Let’s take a look at the option chain for Tesla. The chain lists each option with a 3/18/2022 expiration date, ordered by ascending strike prices. The strike price values range from $750 to $785. At the time this article was written, Tesla stock was trading at $766.37 per share. For the purpose of this exercise, let’s focus on the numbers in the columns outlined in red–the strike price (left) and option price (right).

First, let’s calculate the intrinsic value of the call option with the $750 strike price (see line 1). Remember, the underlying stock currently trades at a price of $766.37. We can calculate the intrinsic value for this option by taking the current price of the underlying and subtracting the strike price. This results in an intrinsic value of $16.37.

We also notice that this contract commands a market price of $35.10, meaning that the contract trades at a premium of $18.73 to its intrinsic value. The market is pricing in this extrinsic value due to uncertainty surrounding the future price of the underlying. They believe that the price of the underlying shares could move enough between the current date and expiration to justify the price of the option beyond its intrinsic value.

We can isolate the volatility component of extrinsic value by comparing two contracts with a similar amount of intrinsic value. In our example, we’ll compare an AAPL call to taTSLA call. Recall that in our previous example, TSLA exhibited a beta whose value amounted to almost twice the value of AAPL’s. We can therefore intuit that an AAPL call option whose intrinsic value and expiry are identical to equivalent properties of a TSLA call option would trade at a lower price.

In line three of the option chain above, we see a quote for an AAPL call option whose strike price and expiration match the price and expiration of the TSLA call in our previous example. Given that AAPL shares currently trade at $150.62, we know that the intrinsic value of the option equals $16.62. The extrinsic value, or the remaining value of the option after subtracting the intrinsic value from the option’s quoted price of $22.60, equals $5.98. This figure amounts to far less than the $18.73 in extrinsic value that a TSLA contract of similar intrinsic value commands. The difference in extrinsic values can be explained by the fact that traders assign greater expectations of future volatility for TSLA stock relative to AAPL stock.

Finally, to illustrate the time component of an options contract, let’s look at the example of the TSLA contract depicted in the image below. This example is similar in nearly every way to the previous one, except that the contract is set to expire one week later on 3/25/2022.

While this new option also offers the right to buy TSLA at the identical strike price of $750, it expires a full week later,,which results in its price being $13.76 greater than the 3/18/2022 contract. We can attribute all of this difference to the time value component of extrinsic value because by comparing two contracts that share the same underlying security, we can be sure that the volatility and intrinsic value are identical.

Options are a sophisticated asset class that offer traders unique opportunities to express bets on both the direction of a security and its future volatility. Traders who want to incorporate options strategies into their approach will benefit from understanding how they are priced. The value of an options contract can be broken down into two key components: extrinsic value and intrinsic value. The ability of a trader to understand the drivers behind both of these components is critical to a trader’s success in options trading.

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