Put-Call Parity
Put-call parity is the no-arbitrage relationship linking the prices of a European call and put with the same strike and expiration to the underlying and a bond.
Formally, C − P = S − K·e^(−rT): a call minus a put equals the underlying price minus the present value of the strike. If the relationship breaks, arbitrageurs can lock in a riskless profit.
Parity explains why synthetic positions work — a long call plus a short put equals long stock — and underpins option pricing.
Example. With the stock at $100, a 100-strike call at $5, and rates near zero, the same-expiry 100-strike put should trade near $5 so that C − P ≈ S − K.
FAQ
What is the put-call parity formula?
C − P = S − K·e^(−rT), where C and P are the call and put prices, S the spot, K the strike, r the rate, and T the time to expiration.
Why does put-call parity matter?
It enforces consistent option pricing and lets traders build synthetic positions; violations create arbitrage opportunities.