Put-call parity is a fundamental principle in options pricing that defines the relationship between the price of a European call option and a European put option with the same strike price and expiration date. It states that the price of a call plus the present value of the strike price must equal the price of the corresponding put plus the current stock price.

The formula is: C + PV(K) = P + S, where C is the call price, PV(K) is the present value of the strike price discounted at the risk-free rate, P is the put price, and S is the current stock price. If this relationship does not hold, there is a theoretical arbitrage opportunity that traders can exploit.

In practice, small deviations from parity are common due to transaction costs, bid-ask spreads, and the difference between European and American options. Significant deviations, however, may indicate mispriced options. This calculator uses continuous compounding to discount the strike price: PV(K) = K × e^(-r × t).

Formulas

PV(K) = Strike × e^(-r × t)

Theoretical Call = Put + Stock - PV(K)

Theoretical Put = Call - Stock + PV(K)

Parity Difference = (Call + PV(K)) - (Put + Stock)

Example

With a call at $5.50, put at $3.00, stock at $100, strike at $100, risk-free rate of 5%, and 30 days to expiration, the present value of the strike is $100 × e^(-0.05 × 30/365) = $99.59. The theoretical call is $3.00 + $100 - $99.59 = $3.41. The theoretical put is $5.50 - $100 + $99.59 = $5.09. The parity difference shows any mispricing.