Split an option's price into time value and intrinsic value
The idea
An option's price is the sum of intrinsic value - what exercising now would yield, floored at zero - and time value, the additional amount buyers pay for the chance of a favourable move before expiry. Time value is greatest when the option is at the money, because that is where uncertainty about the final outcome is highest, and it decays toward zero as expiry approaches. The decay is not linear: it accelerates in the final weeks, which is why time value is described as wasting rather than amortising evenly.
Formulas
Intrinsic value and time value
option price = intrinsic value + time value
- intrinsic value
- what the option would pay if it expired now, never below zero
- time value
- everything else in the price - what the remaining time might yet do
Time value falls to zero at expiry, and does so faster as expiry nears. An out-of-the-money option has no intrinsic value and still has a price, which is entirely time value.
A practice question
What is the intrinsic value of a call with an exercise price of 30 when the underlying trades at 26?
- Zero - correct
- Minus 4Why not: Intrinsic value is floored at zero; the holder simply declines to exercise rather than realising a negative amount.
- 4Why not: The gap is in the wrong direction: the underlying is below the strike, so exercising would cost four rather than gain it.
Intrinsic value is what an option would pay if used right now. A call gives the right to buy at the exercise price. Call intrinsic value = max(S − X, 0) = max(26 − 30, 0) = max(−4, 0) = 0. Buying at 30 when the market price is 26 would be silly, so the holder simply does not use it, and the value cannot be negative. The option can still have a positive price, which is entirely time value, the chance that the price rises before expiry.
A harder one
A call with a strike of 60 trades at 7 while the underlying is at 63. What is its time value?
- 7Why not: The whole premium, which is intrinsic value and time value together.
- 3Why not: The intrinsic value, 63 less 60. Time value is what remains of the premium after that.
- 4 - correct
Premium = Intrinsic value + Time value, so Time value = Premium - Intrinsic value. Intrinsic value of a call = Max(0, Price - Strike) = 63 - 60 = 3. Time value = 7 - 3 = 4. The 4 is what buyers pay for the time left before expiry. The 7 is the whole premium and the 3 is only the intrinsic value.
The hardest tier
Why does a deep in-the-money option have little time value?
- Because it is close to expiryWhy not: Moneyness and time remaining are separate. A deep in-the-money option with a year to run also carries little time value.
- Because its premium is highWhy not: The premium is high because the intrinsic value is large, which says nothing about the time component.
- Because the outcome is nearly certain - correct
Time value = Premium - Intrinsic value. A deep in-the-money option already has a large payoff if exercised. The outcome is nearly certain, so there is little uncertainty left to pay for. It behaves almost like the underlying asset itself. Its premium is mostly intrinsic value, which is a separate matter from how close it is to expiry. This is true even if a year is left.
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