Intrinsic vs extrinsic value: can extrinsic ever exceed intrinsic?
Every option price is two parts: intrinsic value (how far in the money it is) and extrinsic value (time plus implied volatility). Can extrinsic beat intrinsic? Easily, any out-of-the-money option is 100 percent extrinsic. But can a high-IV out-of-the-money call be worth more than an in-the-money call on the same expiration? No, and that one is an arbitrage iron law.
Start with the easy half. Any out-of-the-money option has zero intrinsic, so it is all extrinsic. Even in-the-money options can carry more extrinsic than intrinsic when there is plenty of time left or IV is hot. At the money is almost pure extrinsic. Extrinsic only shrinks next to intrinsic when you go deep in the money and close to expiration.
Now the deeper question, sold to close, not exercised: could a high-IV out-of-the-money call be worth more than an in-the-money call on the same expiration? No. For the same stock and expiration, a call gets cheaper as the strike goes up. Always.
Why is that ironclad? If a higher-strike call ever cost more than a lower-strike one, you would buy the cheap in-the-money, sell the pricey out-of-the-money, and collect a credit on a spread that can only pay you zero or more. Free money. The market erases that instantly.
And cranking IV does not save it. High IV lifts extrinsic at every strike, pumping the in-the-money option right alongside the out-of-the-money one, and the in-the-money still carries its intrinsic on top. Both rise, the order never flips. The only place an out-of-the-money option holds more time value than an in-the-money one is across different expirations, where it simply has more time.