Expiration

Exam items lean on the payoff at expiration, where time value is zero so an option is worth exactly its intrinsic value — calls pay max(0, S − X), puts max(0, X − S). The classic vignette gives you the spot at expiry and asks for the buyer’s or seller’s profit; the “tell” is that you must subtract the premium — the Level I convention is simply profit = payoff − premium (a few treatments compound the premium to its future value, but the exam formula does not). A frequent trap pairs this with the European-vs-American distinction: early exercise only matters before expiry, so at the terminal date both styles collapse to the same intrinsic-value payoff.

Don’t confuse an option’s expiration outcome with a futures settlement: at expiry the futures price converges to spot, but daily mark-to-market has already settled gains along the way, so there is no lump premium and no “expire worthless” branch — the obligation is symmetric, unlike an option’s one-sided right. Memory hook: at expiration, time value dies but intrinsic value pays — only the money already in the money survives.