Why More Financial Optionality Usually Cannot Reduce Holder Value

Summary

The document asks whether adding optionality to a financial instrument can reduce its value, drawing an analogy to Braess's paradox, where adding choices can worsen a system-wide outcome. The accepted answer focuses on a single decision-maker: if the original portfolio remains among the choices, the holder can select whichever available portfolio has the greatest value. Under those conditions, expanding the choice set cannot lower the holder's value.

A second, brief reply suggests the possibility of an option to lend at a negative interest rate, but does not develop or analyze the example. The discussion therefore provides a basic choice-set argument rather than a pricing model, proof under detailed market assumptions, or evidence about interactions among multiple participants. Its conclusion applies to the individual holder's available choices; it does not establish that added optionality must improve outcomes for every participant or at the level of an entire market.

Key ideas

• If the original portfolio remains available, a holder can ignore any newly added choices.
• A decision-maker who selects the most valuable available portfolio cannot lose value solely from a larger choice set.
• The accepted answer addresses an individual holder rather than market-wide effects among participants.
• The suggested negative-rate lending example is raised but not explained or evaluated.

Tags

# Braess's paradox in quantitative finance: When optionality leads to lower value...?


# Braess's paradox in quantitative finance: When optionality leads to lower value...?












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?

## Answer by Mark Joshi (score 2, accepted)

https://quant.stackexchange.com/a/17531

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.

## Answer by rupweb (score 0)

https://quant.stackexchange.com/a/17530

Maybe something like the option to lend money at negative interest would bring about a lower optionality value...

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.