Moneyness, Intrinsic & Time Value

You already know an option’s price has a name: the premium. What you might not know is that the premium is secretly two numbers wearing one coat. Crack it open and you find intrinsic value (what the option is worth right now, this instant) and time value (what you pay for the hope it gets better before the clock runs out). Every option price — from a penny lottery ticket to a deep, sober blue-chip call — is just those two numbers stacked on top of each other.

Getting comfortable with that split is the difference between “the option went up, I guess” and actually understanding why a stock can rise while your call quietly bleeds. Let’s pry the premium apart.

Premium = intrinsic value + time value

The master equation of option pricing is almost embarrassingly simple:

$\text{Premium} = \text{Intrinsic value} + \text{Time value}$

Think of buying a half-built house. Intrinsic value is what the materials and finished rooms are worth today if you sold as-is. Time value is the extra you’d pay because the builder might finish it beautifully before the deadline — you’re paying for the option on a better outcome. If the deadline arrives with nothing built, that extra evaporates and you’re left with only what physically exists.

Time value is also called extrinsic value — same thing, fancier word. “Extrinsic” literally means “from the outside”: it’s the value that comes from things outside today’s price, like how much time is left and how wildly the stock might move. Whenever someone says extrinsic value, mentally swap in “time value” and you’ll be fine.

When the split matters

If you’re a buyer, you want to know how much of your premium is hope (time value), because hope is exactly the part that decays to zero. If you’re a writer (seller), time value is the part you get to keep as the clock ticks. Same option, opposite feelings about that second number.

Intrinsic value: what it’s worth right now

Intrinsic value is the profit you’d lock in if you could exercise the option this instant and immediately close the position. The formulas:

$\text{Call intrinsic} = \max(S - K,\ 0) \qquad \text{Put intrinsic} = \max(K - S,\ 0)$

where $S$ is the current stock (spot) price and $K$ is the strike. The $\max(\dots,0)$ is the whole trick: intrinsic value can never be negative. An option is a right, not an obligation — if exercising would lose money, you simply don’t, and the “value” of that choice floors at zero.

Worked example — a call. Stock at $S = 112$ (i.e. $112), strike $K = 100$. A call lets you buy at $100 something worth $112, so:

$\max(112 - 100,\ 0) = \max(12,\ 0) = 12$

That’s $12 of intrinsic value.

Worked example — a put. Stock at $S = 88$ (i.e. $88), strike $K = 100$. A put lets you sell at $100 something worth only $88:

$\max(100 - 88,\ 0) = \max(12,\ 0) = 12$

That’s $12 of intrinsic value too — a put gains as the stock falls below the strike.

Now flip the put’s stock to $S = 112$. The math gives $\max(100 - 112, 0) = \max(-12, 0) = 0$, i.e. $0. Selling at $100 when the market pays $112 is a terrible idea, so you don’t — and intrinsic value bottoms out at zero rather than going negative.

Moneyness: ITM, ATM, OTM

Moneyness is jargon for “where is the stock relative to the strike?” — and it tells you instantly whether an option has intrinsic value. Three buckets:

• In-the-money (ITM): intrinsic value > 0. Exercising now would pay off.
• At-the-money (ATM): $S \approx K$. The stock sits right on the strike; intrinsic is essentially zero but the option is on a knife’s edge.
• Out-of-the-money (OTM): intrinsic value = 0. Exercising now is pointless.

The catch beginners trip on: ITM means opposite things for calls and puts. A call wants the stock above the strike; a put wants it below. Here’s the full map:

Worked example. Take a $100 strike. Classify both a call and a put at three spots:

Notice the mirror symmetry: at any spot, if the call is ITM the put is OTM, and vice versa. They can only be ATM together, when the stock is sitting exactly on the strike.

Time (extrinsic) value: paying for the chance

If intrinsic value is what an option is worth today, time value is everything else in the price — the premium people pay for the possibility the option ends up worth more before it expires:

$\text{Time value} = \text{Premium} - \text{Intrinsic value}$

Worked example. A $100 call trades at $7 with the stock at $104.

• Intrinsic: $\max(104 - 100, 0) = 4$, i.e. $4.
• Time value: $7 - 4 = 3$, i.e. $3.

So $4 of the premium is “real” exercise-now value and $3 is pure hope — the market’s bet that $104 might become $110 before expiry.

Here’s the surprising part: time value is largest at-the-money and shrinks as you go deep ITM or far OTM. Why? Right at the strike, the option is maximally undecided — a small wiggle in the stock flips it from worthless to valuable, so the uncertainty (and the value of that uncertainty) peaks. Go far OTM and it would take a miracle to matter; go deep ITM and it already behaves almost like the stock itself, with little extra “optionality” left to pay for. The result is a hump: time value is tallest in the middle and tapers off on both sides.

Theta: time decay that melts the premium

Time value has a fatal flaw: it dies. As expiration approaches there’s less and less time for the stock to move your way, so the “hope” portion drains toward zero. At expiry, an option is worth exactly its intrinsic value — every drop of time value is gone.

The Greek letter theta ($\theta$) measures this bleed: how much value an option loses per day purely from the calendar advancing, holding everything else fixed. For a buyer theta is negative (you lose a little each day); for a writer it’s positive (you collect it).

The crucial, counter-intuitive bit: decay is not linear — it accelerates. Time value roughly tracks the square root of time remaining, $\text{TV} \propto \sqrt{t}$. Square roots are steep near zero, so the loss-per-day starts gentle and then falls off a cliff in the final weeks.

A quick feel for $\sqrt{t}$ on a 90-day option worth $10 of time value at the start (value scales as $10\sqrt{t/90}$):

The same calendar month costs you far more time value when it’s the last month than the first. That steepening slope is exactly why option buyers feel fine for weeks and then watch their position evaporate right before expiry.

This is why theta quietly taxes buyers and pays writers. Every day a buyer holds, the hope portion shrinks; the writer who sold that option pockets the difference. A writer who sells an OTM option and watches it expire worthless keeps the entire premium — all of it was time value, and time value always goes to zero at expiry.

Why volatility lives in time value

One last preview. If two otherwise-identical options have different premiums, the gap is almost always in their time value — and the biggest driver of time value (after time itself) is volatility: how much the market expects the stock to move. More expected movement means a fatter chance the option swings into the money, so buyers pay up: more volatility ⇒ richer time value ⇒ bigger premium.

That’s why a sleepy utility stock’s options are cheap while a meme stock’s cost a fortune at the same moneyness — the time-value slab is simply thicker. We’ll unpack volatility and the rest of the six price drivers in the next lesson; for now, just file away that volatility hides inside time value, never inside intrinsic value.

Recap

You can now take any option price apart: split it into intrinsic (exercise-now value, floored at zero) and time value (premium minus intrinsic, fattest at-the-money), read its moneyness off the spot-vs-strike relationship, and predict how theta will melt that time value — slowly at first, then all at once — until only intrinsic remains at expiry.