Put-Call Parity
The arbitrage law that locks call and put prices together at the same strike.
Definition
Put-call parity is the fixed relationship between the prices of a European call and put at the same strike and expiry. It states that holding a call and selling a put (both at strike K) replicates owning the underlying via a forward, so their prices cannot drift apart without creating risk-free arbitrage.
Formula
C + K×e-rt = P + S
Where C is the call price, P is the put price, S is the spot price, K is the strike, r is the risk-free rate, and t is time to expiry. The term K×e-rt is the present value of the strike.
Why it matters
Parity is the backbone of options pricing. It lets you build synthetic positions (a synthetic long stock from a long call plus a short put), back out a fair price for one leg from the other, and detect mispricing. If the equation breaks, arbitrageurs step in until it is restored, which is why screen prices respect it closely.
Example
If a stock trades at 1,000, the 1,000-strike call is 30, and the risk-free PV of the strike is roughly 1,000, then parity implies the 1,000-strike put should be about 30 as well. If the put quoted 40 instead, a trader could lock a near risk-free profit by trading the cheaper synthetic against the richer one.
See it live
Line up matching calls and puts at each strike on TradePulse's live option chain to sanity-check parity yourself.