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There are many funds (index funds or actively managed funds) that charge management fees, which inherently makes it underperform the asset it holds.

There are some applications where finding the derivative value based on those funds is meaningful.

I wonder was there an accepted way to find a risk-neutral measure for those scenarios? Thanks.

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    $\begingroup$ If $I$ is the index and $C$ is the fees (constant), what is the payoff of the say call option? $Max(I-C-K,0)$? $\endgroup$
    – Arshdeep
    Commented Aug 23, 2023 at 20:26
  • $\begingroup$ @Arshdeep I have considered adding the fee directly to the underlying asset, but I am not sure if it is in the risk-neutral spirit as people are willing to pay the fee $\endgroup$ Commented Aug 24, 2023 at 0:31
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    $\begingroup$ I understand, but I want to know the contractual payoff to be able to answer. It would be independent of any modeling assumptions. (unless your question is how to design a derivative contract) $\endgroup$
    – Arshdeep
    Commented Aug 24, 2023 at 20:09
  • $\begingroup$ @arshdeep my background is more life insurance related, and some life insurance payoff is related to how the underlying funds perform, and thus Embedded value (somehow related to fair value) of how the contract emerge is related to asset performance $\endgroup$ Commented Aug 28, 2023 at 3:02

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Ja, good question. Bear with me for a moment:

I used to price options on funds in the context of variable annuity pricing/hedging. Basically a VA is a fund (actually fund of funds) with a guarantee component. The cost of the guarantee, and the management fees, is deducted from what is called the account value, which you can think of as the NAV of the Fund/FoF.

So then the question arose, how do you treat this deduction from the fund value. As a 'dividend yield' or not? I cannot divulge trade secrets, even stale ones, but if you think about it you are getting something of value in return for this deduction. In the VA case you get the guarantee in addition to stellar performance of the funds that are being managed. From that perspective it makes sense, from a risk-neutral point of view, to treat the deductions as a dividend yield. After all you do get something in return, even if only scale of economies.

As for the 'stellar performance' of index trackers? Yeah, let's not talk about that, it's a risk neutral world after all, not real world where the performance is actually sub-par.

I am curious how others will answer this question on the pricing of fund derivatives.

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  • $\begingroup$ I, too, am working on something related to insurance, unit-link products, and universal lives. Things can really get interesting if I want to make existing working more mathematically rigorous, though at the end of the day it is not that meaningful if not even the regulator can understand it. $\endgroup$ Commented Sep 1, 2023 at 14:19
  • $\begingroup$ @PrestonLui Yes at the end of the day you need to explain to your regulator, and the simpler the explanation the better. $\endgroup$
    – Frido
    Commented Sep 1, 2023 at 14:31

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