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What is the name for an option with mandatory exercise but where the holder can choose the exercise date? Is this even an option since there is mandatory exercise?

Mainly interested in a situation where the option holder will claim something at an unknown time in the future without an end date (perpetual).

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    $\begingroup$ If there is no end date can we say that exercise is mandatory ? $\endgroup$
    – Kurt G.
    Apr 6 at 9:15
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    $\begingroup$ "American Perpetual Option" $\endgroup$
    – nbbo2
    Apr 6 at 10:18
  • $\begingroup$ @kurtG. Good point. However, the value of the contract is non-negative for the whole term. Therefore, it is not mandatory, however the contractholder can only exercise the related right. This will they do, since it has a non-negative value. $\endgroup$
    – Cardinal
    Apr 11 at 7:44
  • $\begingroup$ @Cardinal . This sounds like something no one has ever heard before. I do not think it is very important to search for an existing name of this or we can do this later. If you still have things that are unclear to you you may wish to describe everything in full detail, including what asset class that is. $\endgroup$
    – Kurt G.
    Apr 11 at 7:49

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I believe this is sometimes called a flexible forward contract. It is more like a forward than an option, since exercise by the final date is mandatory. The holder does have timing optionality though.

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  • $\begingroup$ Another thing to investigate are timer options, which were popular around 2008/9 which also have the floating maturity property. $\endgroup$
    – river_rat
    Apr 6 at 21:26

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