Put-call parity

Quantitative Finance Glossary

Static no-arbitrage relation between European call and put of identical strike and expiry: C - P = S_0 - K,e^-rT for a non-dividend-paying underlying, generalising to C - P = S_0,e^-qT - K,e^-rT with continuous dividend yield q. Derives from the model-free identity payoff: max(S_T - K, 0) - max(K - S_T, 0) = S_T - K. The cleanest market-data sanity check on option screens: parity violations larger than the bid-ask are not arbitrage opportunities, they are stale prints or hard-to-borrow stocks.

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