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One of the standard tenets of quantitative finance is that options should have an intrinsic value because optionality as such (in the sense of having more choices) should bring about value.

This seems to make sense intuitively - yet intuition can sometimes be misleading as we all know: Braess's paradox is called a paradox because here additional choices (i.e. options) can lead to worse overall performance, i.e. reducing the value for all participants.

My question
Are you aware of (theoretic or special) situations where additional optionality in instruments of quantitative finance (e.g. some exotic options or in some pricing models) could lead to lower value?

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if only one person can make a choice, it strikes me as unlikely that it can reduce value. Ultimately, a choice means that the holder can choose between one of a number of portfolios on a given date. They will choose the one of maximal value. As long as the without choice portfolio was one of the ones they could have chosen, value can only go up.

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  • $\begingroup$ when you say "unlikely" do you mean "still possible" or "impossible"? $\endgroup$ – vonjd Apr 26 '15 at 12:25
  • $\begingroup$ Well the whole point of the braess paradox is that there are other participants and you have to anticipate their reactions to your choice. $\endgroup$ – Chan-Ho Suh Apr 26 '15 at 17:07
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    $\begingroup$ It's hard to say something is impossible without a very clear problem statement. There are situations where multi-player games come into finance and in those cases maybe something like the Braess paradox can occur. $\endgroup$ – Mark Joshi Apr 26 '15 at 22:06
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Maybe something like the option to lend money at negative interest would bring about a lower optionality value...

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    $\begingroup$ If you give someone the option to lose money, he will simply not exercise it. That does not decrease the value of the deal. $\endgroup$ – AFK Apr 26 '15 at 17:13
  • $\begingroup$ well yes, although recently some central bank discount windows have touched negative rates, in other words they are exercising such an option.... $\endgroup$ – rupweb Apr 27 '15 at 15:02
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    $\begingroup$ Just because the rate is negative does not mean you are making a losing choice. You have to consider the cost of the alternative like buying a huge warehouse to keep piles of cash. $\endgroup$ – AFK Apr 27 '15 at 16:40

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