Put-call parity
Principles of Finance glossary · Time Value of Money
Definition
The no-arbitrage relationship among European call and put premiums on a non-dividend stock: C - P = S_0 - K · e^-rT, where K is strike, T is time to expiry, and r is the continuously compounded risk-free rate.
Put-call parity in plain English
Put-call parity is a rule that says a call option and a put option on the same stock aren't independent — their prices are locked together, because otherwise you could build a risk-free money machine (an 'arbitrage'). The idea: owning a call plus a chunk of safe cash gives you the exact same future payoff as owning a put plus the stock itself, so those two bundles must cost the same today. The formula C - P = S_0 - K · e^-rT just writes that balance out, where C and P are the call and put prices, S_0 is today's stock price, K is the agreed strike price, and K · e^-rT is what that strike is worth in today's dollars after shrinking it for interest over time T. If the two sides ever drifted apart, traders would instantly pounce and buy the cheap side, which snaps the prices back into line.
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