Intrinsic value and time value

Two parts of one price

• Intrinsic value is the payout at today's forward F: max(F − K, 0) for a call, max(K − F, 0) for a put. Only an in-the-money option has any.
• Time value, also called extrinsic value, is premium − intrinsic value. It pays for the possibility that the price ends up somewhere better before expiry.

An out-of-the-money option is all time value. An at-the-money one is too, and carries the most of it. A deep in-the-money option is mostly intrinsic value with a thin layer of time value on top. BOSS measures intrinsic value against each expiry's own forward, the price the venue values its options from, not against spot.

How time value behaves

Time value is largest at the money, where the outcome is most uncertain, and shrinks as the strike moves away in either direction. It also shrinks with time, and not in a straight line. With a $100,000 forward and 50% implied volatility, the at-the-money call is worth:

Days to expiry	ATM premium (all time value)
60	$8,070
30	$5,710
7	$2,760
1	$1,040

Time value scales roughly with the square root of the time left, so it melts fastest in the last days. That decay is theta. It also rises and falls with implied volatility, which is what vega measures. At expiry, time value is zero and every option is worth exactly its intrinsic value.

A worked example: guts versus strangle

Guts strategies are built entirely from in-the-money options, which makes the split easy to see. With a 30-day forward of $100,000 and a flat 50% volatility:

• A long guts buys the $95,000 call for $8,420 and the $105,000 put for $8,690: $17,110 in total.
• Intrinsic value: $5,000 in the call plus $5,000 in the put, $10,000. Time value: $3,420 + $3,690 = $7,110.
• Anywhere between the two strikes, the pair pays exactly $10,000 at expiry (the call pays S − $95,000 and the put $105,000 − S, which add up to $10,000). So the maximum loss is $17,110 − $10,000 = $7,110: the time value paid, nothing more.
• Breakevens: below $95,000 only the put pays, so profit is zero at $105,000 − $17,110 = $87,890; above $105,000 only the call pays, so it is zero at $95,000 + $17,110 = $112,110.

Now the long strangle on the same strikes: the $105,000 call for $3,690 and the $95,000 put for $3,420, $7,110 in total, all time value. Its breakevens are $95,000 − $7,110 = $87,890 and $105,000 + $7,110 = $112,110, the same as the guts. The guts costs $10,000 more up front and gets exactly $10,000 more back at expiry: the intrinsic value is just money passing through. What both positions are really buying is the same $7,110 of time value. That is put-call parity at work; in a live market, the wider bid-ask spreads on in-the-money strikes make the guts a little more expensive to trade.

The short guts is the mirror image: it collects $17,110, keeps $7,110 at most, and its loss grows without limit on a rally; on a fall it is bounded, at most $105,000 − $17,110 = $87,890 if BTC went to zero.

Why it matters

Only time value is at stake in whether an option "pays for itself". A buyer needs the move to beat the time value paid; a seller is paid the time value for taking the risk. When comparing strategies, compare the time value bought or sold, not the headline premium.