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Put Call Parity

Put Call Parity is a commonly referenced term
According to Put Call Parity, simultaneously owning a short European put and long European call on the same underlier with the same strike will result in the same return as holding one forward contract on the same underlier.
Put Call Parity demonstrates the relationship between European put and call options with the same underlier, expiration, and strike. The Put-Call parity approach only applies to European-style options since American-style options can be executed at any moment before they expire.
The put-call parity principle works on a few other assumptions, such as:
  • The interest rate is constant and does not vary over time
  • There are no transfer restrictions because the underlying stock is liquid.
You can determine put-call parity by using the formula:
Call option (C) + Present value of strike price PV(x) = Put option (P) + Underlying Asset price (S)
If we move the equation around to C = P + S - PV(x), we can see that the call option should be equal to a portfolio with a long position on the put option, a long position on the underlying asset price, and a short position in the present value of the strike price.

Arbitrage Opportunities

Put-call parity can be used to identify arbitrage opportunities in the market. In this case, an arbitrage opportunity arises when one side of the put-call parity equation is not equal to the other. A trader might use arbitrage to make a profit.