# The Importance of Time Value in Options Trading

Intrinsic Value vs. Time Value
In-the-money Out-of-the money At-the-money
Put/Call Time-value decreases as an option gets deeper in the money; intrinsic value increases. Time-value decreases as an option gets deeper out of the money; intrinsic value is zero. Time-value is at a maximum when an option is at the money; intrinsic value is zero.

## Time-Value Decay

In the figure below, we simulate time-value decay using three at-the-money S&P 500 call options, all with the same strikes but different contract expiration dates. This should make the above concepts more tangible. Through this presentation, we are making the assumption (for simplification) that implied volatility levels remain unchanged and the underlying asset is stationary. This helps us to isolate the behavior of time value. The importance of time value and time-value decay should thus become much clearer.

Taking our series of S&P 500 call options, all with an at-the-money strike price of 1,100, we can simulate how time value influences an option’s price. Assume the date is Feb. 8. If we compare the prices of each option at a certain moment in time, each with different expiration dates (February, March, and April), the phenomenon of time-value decay becomes evident. We can witness how the passage of time changes the value of the options.

The figure below illustrates the premium for these at-the-money S&P 500 call options with the same strikes. With the underlying asset stationary, the February call option has five days remaining until expiry, the March call option has 33 days remaining, and the April call option has 68 days remaining.

As the figure below shows, the highest premium is at the 68-day interval (remember prices are from Feb. 8), declining from there as we move to the options that are closer to expiration (33 days and five days). Again, we are simply taking different prices at one point in time for an at-the-option strike (1100), and comparing them. The fewer days remaining translates into less time value. As you can see, the option premium declines from \$38.90 to \$25.70 when we move from the strike 68 days out to the strike that is only 33 days out.

The next level of the premium, a decline of 14.7 points to \$11, reflects just five days remaining before expiration for that particular option. During the last five days of that option, if it remains out of the money (the S&P 500 stock index below 1,100 at expiration), the option value will fall to zero, and this will take place in just five days. Each point is worth \$250 on an S&P 500 option.

One important dynamic of time-value decay is that the rate is not constant. As expiration nears, the rate of time-value decay (theta) increases (not shown here). This means that the amount of time premium disappearing from the option’s price per day is greater with each passing day.

The concept is looked at in another way in the figure below: The number of days required for a \$1 (1 point) decline in premium on the option will decrease as expiry nears.

This shows that at 68 days remaining until expiration, a \$1 decline in premium takes 1.75 days. But at just 33 days remaining until expiration, the time required for a \$1 loss in premium has fallen to 1.28 days. In the last month of the life of an option, theta increases sharply, and the days required for a one-point decline in premium falls rapidly.

At five days remaining until expiration, the option is losing one point in just less than half a day (0.45 days). If we look again at the Time-Value Decay figure, at five days remaining until expiration, this at-the-money S&P 500 call option has 11 points in premium. This means that the premium will decline by approximately 2.2 points per day. Of course, the rate increases even more in the final day of trading, which we do not show here.

## How Is an Option’s Time Decay Measured?

Options traders use the Greek value Theta (Θ) to measure time decay, and interpret it as the dollar change in an option’s premium given one additional day to expiration, all else equal. Therefore, an option with a premium of \$2.30 and a theta of \$0.05 will be worth \$2.25 the next day, assuming nothing else changes.

## Which Options Have the Greatest Time Value?

At-the-money options have the greatest time value (and are also most sensitive to time decay, as measured by theta). Moreover, options approaching expiration see their time decay accelerate the fastest relative to those with longer expirations remaining.

## Why Is Time Value of Options Also Called Extrinsic Value?

An option’s premium is composed of two parts: intrinsic and extrinsic value. Intrinsic value is the amount of money the option contains if it were exercised immediately. For instance, a 30-strike call allows you to buy shares at \$30, and if the stock is trading at \$35, there has to be \$5 of intrinsic value in that call. Extrinsic value is anything above the intrinsic value. So, if you instead owned the 40-strike call when the stock is trading at \$35, it wouldn’t be worth anything to exercise at the moment. But, there will still be a premium, or the extrinsic value, which is based on the chances that this option will pan out before expiration. This is based on the time value of the option, since the more time there remains, the more chances the stock will rise above \$40.

## The Bottom Line

While there are other pricing dimensions (such as delta, gamma, and implied volatility), a look at time-value decay is helpful to understand how options are priced.