How to calculate Put-Call Parity

Put-Call Parity can be described as the relationship between the price of a put option and a call option and relates mainly to European call and put options. The Put-Call Parity is an option pricing concept that requires the values of call and put options to be in equilibrium to prevent arbitrage.

How does it work

A close link Prices of put options, call options, and their underlying stock are very closely related. A change in the price of the underlying stock affects the price of both options that are written on it, and the put-call defines parity in the relationship. The relationship is specific, such that a combination of any two components yields the same profit or loss profile as the third instrument. The Put-Call Parity says that if all these three instruments are imbalanced, then there is no arbitrage opportunity.

The formula

The full version The Put-Call Parity can be expressed as follows: P(S,t) + S(t) = C(S,t) + K * e-r (T-t) P (S,t) is the price of the put option when the current stock price is S and the current date is t
. S(t) is a stock's current price. - 
C (S,t) is the price of the call option when the current stock price is S and the current date is t
. K is the strike price of the put option and call option
. - B (t) is the price of a risk-free bond
. - r is the risk-free interest rate
. - t is the current date. 
 - T is the expiration date of a put option and a call option. The put-call parity is a representation of two portfolios that yield the same outcome. Put option + stock = call option + bond Protection from arbitrage The left side represents a portfolio consisting of a put option and a stock. The right side represents a portfolio consisting of a call option and a bond. It does not matter whether the price of the underlying stock rises or falls, both sides of the equation are balanced.
A final word If a portfolio on one side of the equation was cheaper, it could be bought and the portfolio on the other side sold and profit made from a risk-free arbitrage.