Why is it stated sometimes that $C - P = F$

and in wikipedia it statest that $C - P = D(F-K)$, where D is the discount factor and K is the strike (of both the call and put?).

Is this just affected by whether the option is on a future or on spot?

  • $\begingroup$ I have never seen the first version of the put call parity. As it would imply no debt needed. Could you clarify where you saw that? $\endgroup$ – phdstudent Apr 29 '18 at 14:28
  • $\begingroup$ Quant Job Interview Questions and Answers, Joshi, pg 39 Solution to Question 2.15 $\endgroup$ – Trajan Apr 29 '18 at 14:44
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    $\begingroup$ That's probably a notation problem. $F$ in the first instance refers to the price of the "forward contract", the contract that pays the price of the asset minus a given strike $K$ at some future date. In the second instance, it refers to the forward price of the asset. $\endgroup$ – Ivan Apr 29 '18 at 20:01
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    $\begingroup$ Agreed. The first statement should be read as "long a call and short a put is equivalent to a forward contract (with the same strike)". The second statement is "the price of a call minus the price of a put is the discounted value of the forward price minus the strike". $\endgroup$ – Alex C Apr 29 '18 at 22:17
  • $\begingroup$ @AlexC I will accept ^^^ if you put it as an answer $\endgroup$ – Trajan May 9 '18 at 17:58

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