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?

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)

No problem @mm12! Glad it solved your problem :)

A CFA Level 2 Discussion About Put-Call Parity For Forwards

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This topic has 6 replies, 2 voices, and was last updated Apr-176:04 am by Sophie Macon.

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- MM12
  Participant
  - 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?
- Sophie 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)
- Sophie Macon
  Keymaster
  20 Apr 2017 at 6:04 am
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  No problem @mm12! Glad it solved your problem 🙂
- MM12
  Participant
  - CFA Level 3
  20 Apr 2017 at 5:54 am
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  @Sophie: Thanks for the answer, that was very helpful!
- MM12
  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!
- MM12
  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.”
- Sophie 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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