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Put-Call Parity for Forwards – help please

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    • Avatar of MM12MM12
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        • CFA Level 3
        19 Apr 2017 at 10:16 pm
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        Hi,

        I’m having trouble understanding the put-call parity for forwards. Specifically, in establishing the put-call parity, the Schweser notes and CFA books state that the payoff of a call option on a forward is max{0,S(T)-X}. Here S(T) is the price of the underlying asset to the forward at time T (expiration of both the call and the forward).

        As I understand it, when the option expires, I have the right (but not the obligation) to buy the forward for X. This forward immediately expires, giving me the obligation to buy the asset for F(T). So should I choose to exercise the option, my total payoff should be S(T)-F(T)-X instead of S(T)-X. What did I do wrong?

      • Avatar of Sophie MaconSophie Macon
        Keymaster
          20 Apr 2017 at 3:10 am
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          Hi @MM12, welcome!
          Before I delve any deeper, I don’t understand why you’re going into options for forwards? I’m not sure if this is covered under CFA syllabus (at least at my time)

        • Avatar of Sophie MaconSophie Macon
          Keymaster
            20 Apr 2017 at 6:04 am
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            No problem @mm12! Glad it solved your problem 🙂

          • Avatar of MM12MM12
            Participant
              • CFA Level 3
              20 Apr 2017 at 5:54 am
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              @Sophie: Thanks for the answer, that was very helpful!

            • Avatar of MM12MM12
              Participant
                • CFA Level 3
                19 Apr 2017 at 10:46 pm
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                Hi again,

                After some more thinking, I now believe I misinterpreted the meaning of an option on a forward – where I first thought it meant that you had the right to enter into a specific predetermined forward at the expiration of the option, I now think that it means you have the right to enter a forward at expiration of the option, and the forward will be priced as of that moment. I was unable to find a clear explanation of options on forwards, so can someone please let me know if this is correct? Thanks!

              • Avatar of MM12MM12
                Participant
                  • CFA Level 3
                  20 Apr 2017 at 3:32 am
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                  Thanks for having a look. Currently for level 2, we have “LOS 50.i: Demonstrate how the put-call parity for options on forwards (or futures) is established.”

                • Avatar of Sophie MaconSophie Macon
                  Keymaster
                    20 Apr 2017 at 4:32 am
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                    I now believe I misinterpreted the meaning of an option on a forward – where I first thought it meant that you had the right to enter into a specific predetermined forward at the expiration of the option, I now think that it means you have the right to enter a forward at expiration of the option, and the forward will be priced as of that moment. I was unable to find a clear explanation of options on forwards, so can someone please let me know if this is correct? Thanks!


                    @mm12                     – option on forward means you have the right to enter the forward at a predetermined strike price (your forward is now the underlying asset, I believe this is the source of your confusion). And for call option on a forward, upon expiry, if the forward price is higher, you exercise your right to purchase that forward at the (lower) strike price to make instant profits.

                    Hope this helps

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