Put-call parity
Quantitative Finance glossary · Derivatives Pricing & Volatility Surfaces
Definition
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.
Put-call parity in plain English
An option is a contract that gives you a choice: a 'call' lets you buy something later at a fixed price, a 'put' lets you sell at a fixed price. Put-call parity is a beautiful fact that these two are secretly linked — if you know the price of one, simple arithmetic gives you the price of the other, because holding a call and selling a put behaves exactly like just owning the stock (minus what you'd pay for it later). The clean version is C - P = S_0 - K,e^-rT, where C and P are the call and put prices, S_0 is today's stock price, K is the fixed price in the contract, and e^-rT just shrinks a future dollar amount down to today's value. Traders use it as a lie-detector: if the two prices don't fit this relation by more than the normal trading gap, it's almost always a stale or messy quote, not free money.
Learn these first
Related Quantitative Finance terms
Quantitative Finance practice questions · Quantitative Finance flashcards · Quantitative Finance study guide