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r > 0. I understand that money today is worth more than money tomorrow. So if volatility is 0, it's better to take the money today. But I don't understand how to square away the following:

  • Time value for American Options is always nonnegative
  • Value = Time Value + Intrinsic Value

How is it ever optimal to throw away positive time value?

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  • $\begingroup$ You are not throwing anything away. You monetise a value that is at least as large as your option that you have when you did not exercise. The time value of the unexercised option exists only on paper, unless you sell it. $\endgroup$
    – Kurt G.
    Commented Mar 27, 2023 at 9:01

1 Answer 1

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“How is it ever optimal to throw away positive time value?”

Answer: when the thing you are throwing away is less than what you are gaining through the early exercise . What is that ? Interest you receive on the strike price by receiving it earlier.

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  • $\begingroup$ So then wouldn't selling (intrinsic + time) to someone else be better than exercising for intrinsic? $\endgroup$
    – Alec
    Commented Mar 27, 2023 at 16:11
  • $\begingroup$ I guess not because then they would exercise right away anyways. So I guess the conclusion is that intrinsic is worth less than the value of early exercise? Because the value of exercising now is actually discounted into the future at rF, so the "value" of exercising now is more than the intrinsic value? $\endgroup$
    – Alec
    Commented Mar 27, 2023 at 17:24
  • $\begingroup$ The first thing you said is key. The person buying from you would immediately exercise anyways. Therefore the option price is no different than exercising it yourself. $\endgroup$
    – dm63
    Commented Mar 28, 2023 at 21:05

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