Moneyness, Intrinsic Value, and Time Value

4.1 Why does a worthless option cost money?

Mint noticed something odd. With BTC at $100,000, a $110,000 call would be worthless if it expired right now: nobody would pay $110,000 for something worth $100,000. Yet it cost $2,765.

"Why would anyone pay for something that's worth nothing?" asked Mint.

"It's worth nothing today," said Hash. "But there are 30 days left, and bitcoin moves a lot. The $2,765 is the price of the chance that it'll be worth something by then. Every option price is made of two parts: what it's worth now, and what it might become."

4.2 Moneyness

Moneyness describes where an option's strike sits relative to the current price.

Moneyness	Call	Put
In the money (ITM)	Strike below current price	Strike above current price
At the money (ATM)	Strike near current price	Strike near current price
Out of the money (OTM)	Strike above current price	Strike below current price

With BTC at $100,000:

Option	Moneyness
$90,000 call	In the money
$100,000 call	At the money
$110,000 call	Out of the money
$110,000 put	In the money
$100,000 put	At the money
$90,000 put	Out of the money

4.3 Intrinsic value

Intrinsic value is what an option would be worth if it expired right now.

Call intrinsic value = maximum of (current price − strike, 0)

Put intrinsic value = maximum of (strike − current price, 0)

Only in-the-money options have intrinsic value. At-the-money and out-of-the-money options have zero intrinsic value.

4.4 Time value

Time value, also called extrinsic value, is everything in the premium beyond intrinsic value. It reflects the possibility that the option becomes more valuable before expiry.

Premium = intrinsic value + time value

Here are 30-day BTC options with BTC at $100,000 and illustrative 55% implied volatility (Chapter 6):

Option	Premium	Intrinsic value	Time value
$90,000 call (ITM)	$12,251	$10,000	$2,251
$100,000 call (ATM)	$6,284	$0	$6,284
$110,000 call (OTM)	$2,765	$0	$2,765
$110,000 put (ITM)	$12,765	$10,000	$2,765
$100,000 put (ATM)	$6,284	$0	$6,284
$90,000 put (OTM)	$2,251	$0	$2,251

Two patterns stand out.

At-the-money options have the most time value. They're the most uncertain: a small move either way decides whether they end up valuable.

Time value shrinks the further an option is from the money, in either direction. A deep in-the-money option behaves almost like the underlying itself, and a far out-of-the-money option is unlikely to become valuable.

"So the out-of-the-money call is pure hope," said Mint. "And the in-the-money call is mostly real value, plus a bit of hope."

"That's a good way to remember it," said Hash.

4.5 Time value decays

At expiry, time value is zero. All that's left is intrinsic value. So time value shrinks as expiry approaches, a process called time decay.

Days to expiry	$100,000 ATM call premium (BTC at $100,000, 55% IV)
90	~$10,862
30	~$6,284
7	~$3,038
0	$0

Notice the decay isn't steady. Going from 90 days to 30 days loses about $4,600. Going from 30 days to 7 days loses about $3,200, in a much shorter time. Decay accelerates as expiry approaches, especially for at-the-money options. Chapter 8 measures this with a Greek called theta.

This is the hidden cost of buying options. Even if the price doesn't move against you, your option loses value every day. Option sellers earn this decay; option buyers pay it.

Chapter 4 · Time value and decay

An option premium splits into intrinsic value and time value, with time value largest for at-the-money options. As the days to expiry fall from 90 to 30 to 7 to 0, the time value decays along an accelerating curve, reaching zero at expiry.

4.6 Put-call parity

Look again at the table in section 4.4. The $90,000 call costs exactly $10,000 more than the $90,000 put. The $110,000 put costs exactly $10,000 more than the $110,000 call.

This isn't a coincidence. A relationship called put-call parity links the prices of calls and puts with the same strike and expiry. In simplified form, ignoring interest rates and funding:

Call price − put price = current price − strike

For the $90,000 strike: $12,251 − $2,251 = $10,000 = $100,000 − $90,000.

If this relationship breaks, arbitrage traders can profit by combining calls, puts, and the underlying, which pushes prices back into line. In practice, crypto options prices are also affected by the futures basis and interest rates (Module 7, Chapter 2), so parity holds relative to the forward price rather than exactly to spot.

You don't need to trade parity. But it explains why calls and puts can't be priced independently, and it's a good sanity check when reading an options chain.

4.7 Why this matters for choosing options

If you buy	You pay mostly for	Behaviour
Deep ITM options	Intrinsic value	Moves almost one-for-one with the underlying; less decay as a share of premium
ATM options	Time value	Most sensitive to time decay and volatility
Far OTM options	Time value only	Cheap, often expire worthless; big percentage gains if a large move happens

"So if I want something that behaves like owning bitcoin, but with a capped loss, I'd buy in the money," said Mint. "And if I want a lottery ticket, far out of the money."

"Roughly," said Hash. "Most traders who keep buying lottery tickets slowly lose to time decay."

4.8 Try it yourself

On a BTC options chain, pick one expiry. For three calls (ITM, ATM, OTM) and three puts (ITM, ATM, OTM), split each premium into intrinsic value and time value. Which has the most time value? Then compare the ATM call's premium across three different expiries and see how time value changes with time remaining.

Finally, check put-call parity on one strike: does call minus put roughly equal the forward or spot price minus the strike?

Key takeaways from this chapter

1. Moneyness describes the strike relative to the current price: in, at, or out of the money.
2. Intrinsic value is what an option is worth if exercised now; only in-the-money options have it.
3. Time value is the rest of the premium, reflecting the chance of becoming more valuable.
4. At-the-money options have the most time value; it shrinks further from the money.
5. Time value decays to zero by expiry, and decay accelerates near expiry.
6. Put-call parity links call and put prices with the same strike and expiry.
7. Deep ITM options behave like the underlying; far OTM options are cheap long shots.