# Put-call parity

Can someone please explain put-call Parity to me. I’m on the tail end of a 9 hr study session and my head hurts. Thank you

That is a bit broad. What are you having problems with?

C-P = S - Kexp(-rt) it’s actually explained really well in Schweser. If you consider two instruments: covered call C - S and protected put P-Kexp(-rt) you will see that their payoff functions are identical. Therefore, their prices should be identical.

I’ve typically seen it expressed (and remember it as): S + P = C + X/(1+r)^T-t —> a protective put = a fiduciary call Basically, you’ve got four securities here to mix and match: - underlying stock (S) - call option on underlying stock © - put option on underlying stock § - risk-free debt security maturing on the option expiration date (X/(1+r)^T-t) So why does anyone care? Well, you can use this relation price any of the four securities, given the values of the other three, and can seek to exploit arbitrage opportunities if the relation doesn’t hold. To what extent does this actually hold in reality, I don’t know. This is also neat in that it provides examples of how to create “synthetic” securities and helps illustrate how an option’s properties affect its value. Anyway, reexamine this tomorrow with a fresh head and I’m confident all will become clear. Good luck on your exam.