Intrinsic value
The value an option would have if exercised immediately: max(0, stock − strike) for calls, max(0, strike − stock) for puts. It can never be negative.
Intrinsic value is the floor under an option’s price — arbitrage keeps American options from trading below it. At expiration, intrinsic value is all that remains; every payoff diagram at expiry is simply intrinsic value minus the premium paid.
The rest of an option’s price, the part above intrinsic, is where all the interesting pricing questions live.
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