Put-Call Parity

The no-arbitrage relationship between European call and put prices: C − P = S·e^(−δT) − K·e^(−rT).

Put-call parity (Stoll, 1969) states that for European options with the same strike and expiry: C − P = PV(F) − PV(K) where PV(F) = S·e^(−δT) is the present value of the forward price and PV(K) = K·e^(−rT) is the present value of the strike. Violation of put-call parity creates a risk-free arbitrage: if C − P > S·e^(−δT) − K·e^(−rT), sell the call, buy the put, buy the stock, and borrow PV(K). Parity holds for European options but can be violated for American options due to early exercise.

Formula

C - P = Se^{-\delta T} - Ke^{-rT}

Related Terms

Delta (Δ)

The sensitivity of an option's price to a $1 change in the underlying spot price.

Protective Put

Owning the underlying and buying a put option as insurance against downside loss.

Covered Call

Owning the underlying asset and selling a call option against it to generate premium income.

Collar

Long stock + protective put (lower K) + covered call (higher K) — bounded return with downside protection.

Black-Scholes-Merton Model (BSM)

The foundational option pricing formula that gives the fair value of a European call or put as a function of spot, strike, rate, volatility, and time.