Put-call parity

La relazione fissa tra una call, una put, l’azione e lo strike che mantiene coerenti i prezzi — violarla apre un arbitraggio.

Put-call parity is the fixed relationship that ties together a call and a put with the same strike and expiration. In plain terms: owning a call plus holding enough cash to buy the stock at the strike ends up worth the same as owning a put plus owning the stock itself. If that balance breaks, the two sides can be traded against each other for a locked-in edge, which is exactly why the relationship rarely drifts far in liquid markets.

In practice you don't need to arbitrage it to benefit from it. It's a sanity check. If a 100-strike call trades at 6 and the matching put trades at 3 with the stock near 100 and rates low, those prices should sit close to parity. When a broker quotes a put that looks strangely cheap next to its call, parity tells you whether it's a real opportunity or just a stale or wide quote you shouldn't chase.

The common mistake is applying the textbook formula to American options on dividend-paying stocks. Parity holds cleanly for European options; early exercise and dividends pull the two sides apart, so a gap isn't always free money. Treat parity as a reference point, not a promise.

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