The intrinsic value is just one part of the premium story.

The other key component of the option premium is the time value.

Even if an option is currently outta the money with zero intrinsic value, it can still have a positive premium due to time value.

So what does the time value actually quantify and what drives it? Time value reflects the risk faced by the option seller due to uncertainty around whether the option will be exercised and how much they might need to pay out.

It's tempting to think that this simply quantifies the risk that the intrinsic value of the option at expiry will be higher than it is now.

And if we work with this assumption for a moment, we can intuitively identify two key drivers of time, value, time to expiry and the volatility of the underlying asset.

Time to expiry should be positively correlated with time value because the longer the time to expiry, the greater the risk that the intrinsic value of the option could increase before expiry.

The same logic applies to volatility.

If the underlying is a stable asset with little price movements, there's relatively little risk that its intrinsic value will change significantly.

However, if the underlying is highly volatile with large price swings, well this increases the risk of significant changes in intrinsic value in the future.

This intuitive view explains why time to expiry and volatility are major drivers of time value.

However, it doesn't explain another observable behavior of time value.

Look at the charts here.

It shows the price of a $100 strike call option across different asset price scenarios at four different stages of its life.

Three months before expiry, two months before expiry, one month before expiry.

And at expiry volatility has been kept constant, so it doesn't play a role here.

The only varying factors are time to expiry and the underlying asset price.

Let's focus on a single asset price scenario to start at an asset price of $100.

At expiry, the option has a value of zero.

Oh, this makes sense because the option has expired and its value at that point consists only of intrinsic value.

Since the option expired at the money, the intrinsic value is zero, and because there's no time left until Expiry time value is also zero one month before expiry. However, at an asset price of $100, the same option has a premium of one $98.

Two months before expiry, the premium was $2.93, and three months before expiry it was $3.59.

As expected, we see a positive correlation between time, value and time to expiry.

The longer the time to expiry, the higher the option premium.

And because all these options were at the money at an asset price of a hundred dollars, the difference in premiums is solely due to changes in time value.

However, when we look at other asset price scenarios, we observe another factor driving time value as well as we consider scenarios where the option is deep in the money, say with a spot price of 120 or deep out of the money, say with an asset price of 80, the lines of the chart converge.

This means the difference in option premiums diminishes as the option moves further in or out of the money, mostly due to this decline in time value.

But why does the time value decrease when an option moves deep in or deep out of the money? To understand why time value decreases when an option moves deep in or out money, we need to consider what time value represents.

Time value reflects the uncertainty around whether the option will be exercised when an option is at the money.

Exercise is highly uncertain, so the time value is high, but as the option moves deep in or deep outta the money, the likelihood of exercise becomes much more predictable.

Therefore, reducing uncertainty exercise will be almost certain if the option is deep in the money.

But exercise is extremely unlikely.

If the option is deep outta the money with less uncertainty, there's less time value, which is why deep in the money and deep outta the money options have lower time value than those at the money.

This understanding of time value aligns with our earlier observations.

Time value increases with longer time to expiry and with higher volatility because both factors raise the risk of significant price, movement potential, and therefore the need for frequent hedge adjustments.

But does this always explain why time value decreases when options are deep in or deep outta the money? Yes. Yes, it does.

Consider an extreme example, a call option expiring Today with a strike price of 100 while the underlying assets trades at 500.

What's the uncertainty around exercise here? Essentially none.

The option will almost certainly be exercised.

This means the seller needs to be fully hedged with no need to adjust their position.

If the price moves further, the option behaves more like a forward contract because the exercise outcome is virtually certain and as we've seen, forwards don't have time value because there's no exercise uncertainty.

To wrap up, here's what we've learned about time value first.

Time value is driven by time to expiry and volatility of the underlying assets.

Second at expiry and options value is solely based on intrinsic value, because time value drops to zero and third time value decreases when options move deep in or deep outta the money.

Because exercise uncertainty diminishes reducing the need for dynamic hedging for the seller.

In essence, time value is the price of uncertainty.

The more unpredictable the path to expiry, the higher the premium and option seller will demand.