CFA CFA Level 2 Put-Call Parity for Forwards – help please

Put-Call Parity for Forwards – help please

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    • MM12
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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?

    • MM12
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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!

    • Sophie Macon
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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)

    • MM12
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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.”

    • Sophie Macon
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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

    • MM12
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      @Sophie: Thanks for the answer, that was very helpful!

    • Sophie Macon
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      No problem @mm12! Glad it solved your problem 🙂

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