What Is a Put-Call Parity?

Put-call parity is a principle in options pricing that demonstrates the relationship between the price of European put and call options of the same class (i.e., the same underlying asset, strike price, and expiration date). It suggests that when discounted to present value, the combined cost of a call option and an underlying asset should equal the combined cost of a put option and the exercise price. The equation is as follows:

C + PV(X) = P + S

C = Price of the call option
PV(X) = Present Value of Strike Price (X)
P = Price of the put option
S = Spot price or current price of the underlying asset

This principle allows traders to create risk-free positions by synthesizing the underlying asset (a long call and a short put) or a risk-free bond (a long put and a short call). Violations of the put-call parity represent arbitrage opportunities in the market.

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