Pricing & Mechanics
Intrinsic and Extrinsic Value
Also called: time value, premium decomposition
An option's price splits into intrinsic value, the amount it is in the money right now, and extrinsic value, everything else: the premium paid for time and volatility. Out-of-the-money options are pure extrinsic value.
For a call, intrinsic value is max(stock − strike, 0); for a put, max(strike − stock, 0). Extrinsic value is the option price minus intrinsic value. It is largest at the money, shrinks as the option moves deep in or out of the money, and decays to zero at expiration.
Extrinsic value is what theta erodes and vega inflates. Option sellers earn it; option buyers pay it and need movement to overcome it. Early exercise of an American option forfeits any remaining extrinsic value, which is why it is rarely optimal except around dividends or for deep in-the-money puts.
Formula
Extrinsic = option price − intrinsic · Call intrinsic = max(S − K, 0) · Put intrinsic = max(K − S, 0)
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Frequently asked questions
Why does an in-the-money option cost more than its intrinsic value?
The extra is extrinsic value, the market's price for the chance the option finishes even deeper in the money before expiration. It approaches zero as expiration nears.