Introduction to Options Pricing

Generic Components of Options Prices

Intrinsic Value

Time Value Premium

Option Price Curves

Generic Components of Options Prices

In the most basic sense, an option has two essential components: Intrinsic Value and Time Value Premium.

Only in-the-money options have intrinsic value, which is defined as the difference between the current price of the underlying security and the option’s strike price. In other words, it is the value that would be derived from the option, were it to expire immediately. For example, a Call option with a strike price of 55.0 on a stock trading at 58.0 has an intrinsic value of $3.00. Options that are trading at-the-money or out-of-the-money have no intrinsic value.

Intrinsic Time Value

The intrinsic value of an option might be calculated thus...

In the case of a Call Option:      Underlying Price - Strike Price = Intrinsic Value*

In the case of a Put Option:      Strike Price - Underlying Price = Intrinsic Value*

* Subject to lower bound of zero (option must be in-the-money in order to have intrinsic value)

Let us illustrate the concept of intrinsic value by looking at a table that depicts the intrinsic value of two options contracts – one a call option and the other a put option – depending on the price of the underlying security.

As can be seen from the table, the intrinsic value of the call with a strike of 50 remains at zero until the stock starts to trade above the strike price. The call intrinsic value is greater than zero, and rising, as the stock starts to move away from the strike price to the upside.

On the other hand, we can also see that the intrinsic value of the put with a strike of 50 remains at zero as long as the stock is trading above 50. The put intrinsic value is greater than zero, and rising, as the stock starts to move away from the strike price to downside.

Let’s look at a graphical representation of the data in the table above. The following is a chart that depicts the intrinsic value of the call that has a strike of 50, and a chart that depicts the intrinsic value of the put that has a strike of 50, respectively, from the current illustration. Note: Please remember that the charts represent intrinsic values (not just profit/loss values, as the most common form of options diagrams do).

As defined earlier, the intrinsic value of an option is the value that can be derived from an option, at expiration. Prior to expiration, however, options almost always trade at a value greater than that of their intrinsic worth. This “premium” to an option’s intrinsic value is known as its time value premium.

The buyer of an option is willing to pay this premium, before expiration, because he/she believes there is a good chance that a favorable change will occur in the price of the underlying security at some point before expiration, and that that change in the price of the underlying will bring about an increase in the price of the option itself. (The seller/writer of the option will, of course, be hoping that the opposite occurs and/or for “time decay”, which we will talk about in another article, to cause the option to decline in value.) 

Time Value Premium

The time value premium of an option might be calculated thus...

In the case of a Call or a Put Option:   Option Price - Intrinsic Value = Time Value*

Let us illustrate the concept of intrinsic value by looking at a table that depicts the intrinsic value of two options contracts – one a call option and the other a put option – depending on the price of the underlying security.

^ We notice an interesting phenomenon with the deeply in-the-money put (when the stock is trading at 41) in this example. The price of this particular put option is actually less than its intrinsic value, implying a negative time value premium. Deeply in-the-money options often show this sort of apparent anomaly, which is a result of the preference that traders have for options that are closer to the money (since they are less expensive) over those that are farther from the money.

Option Price Curves

The following graphs tie together most of the information that we have perused so far in this section. The first graph depicts a Call Option Price Curve, inclusive of its intrinsic value and time value premium components. The graph that follows it depicts a Put Option Price Curve, inclusive of that option’s intrinsic value and time value premium components.

The graph seen above might appear mundane but it is actually quite eloquent. We’ve already spoken about several facets (such as the fact that the intrinsic value line bends at the strike price) that are easily apparent in the graph; however, one aspect that we haven’t touched upon as yet is that of the point at which the time value premium is at its largest.

Let’s direct our attention to the area on the chart that is directly above the strike price (50.0). Notice that the time value premium segment of the graph is at its widest right at the strike price. If we take another close look at the table titled “Changes in Intrinsic & Time Value of a Call and a Put, each with a Strike Price of 50”, above, we find confirmation of this occurrence. The time value of the Call with a strike price of $50 is $3.10, when the stock is trading at $50 (at-the-money). This value is the largest of all the readings of time value on the Call side.

Thus, we can gather that the time value premium on a call option is at its greatest when the option is at-the-money.

Another fact that we can decipher from the chart (and the table) above, is that the call option price curve and the call’s intrinsic value line virtually merge when the stock price is trading at a significant distance from the strike price. In other words, the time value premium grows progressively smaller as the stock price moves away from the strike price.

The graph seen below is that of the generic put option price curve, and also depicts the time value and intrinsic value components of the price of the generic put option.

From this chart of the generic put option price curve, we can see similar concepts to those seen in the chart of the call option curve that we looked at earlier. The time value premium of the put option is at its greatest when the stock is trading at-the-money, and grows progressively smaller as stock trades away from the strike price.

Summary:

The time value premium on an option (call or put) is the greatest when the option is at-the-money.

The option (call or put) price curve and its intrinsic value line virtually merge when the stock is trading at a significant distance from the strike price. In other words, the time value premium on an option (call or put) grows progressively smaller as the stock price moves away from the strike price.