Put-Call Parity
The no-arbitrage relationship linking the prices of a European call and put at the same strike and expiry: C − P = S − K·e^(−rT).
Formula
C − P = S − K·e^(−rT) (European options, no dividends)
Put-call parity is a no-arbitrage identity tying together the prices of a European call and put that share the same underlying, strike, and expiration. It states that holding a call and shorting a put is economically equivalent to holding the underlying financed at the risk-free rate.
The relationship is enforced by arbitrage: if it breaks, a trader can lock in a riskless profit by buying the cheap side and selling the rich side, so market makers keep prices pinned to parity. It also reveals the synthetic equivalences traders rely on — a synthetic long stock is a long call plus a short put at the same strike, and a conversion or reversal trade exploits tiny parity dislocations.
Parity holds cleanly only for European options; American options can deviate because of early-exercise value, and dividends shift the equation (the present value of expected dividends is subtracted from the spot term). It is the backbone check behind most options pricing — Black-Scholes call and put prices must satisfy it exactly.
Example
Stock at $100, 1-year $100 strike, r = 5%. The discounted strike is 100·e^(−0.05) = $95.12, so C − P = 100 − 95.12 = $4.88. If the call trades at $8.00, the put must trade at 8.00 − 4.88 = $3.12 — otherwise an arbitrageur profits.
Related Terms
Black-Scholes Model
The foundational closed-form formula for pricing European options from spot, strike, time, interest rate, and volatility.
AdvancedCall Option
An options contract giving the buyer the right to purchase the underlying asset at the strike price before or on expiration.
BeginnerIntrinsic Value
The immediate exercise value of an option — how much in the money it is right now, ignoring time and volatility.
IntermediatePut Option
An options contract giving the buyer the right to sell the underlying asset at the strike price before or on expiration.
BeginnerStrike Price
The fixed price at which the option holder can buy (call) or sell (put) the underlying asset if they choose to exercise.
Beginner