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Modeling Fund Management Fees as a Dividend Yield in Derivative Pricing

Article Quant Q&A · Author: Preston Lui
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Summary

The document considers how to price derivatives whose underlying fund loses value through management fees. Its answer draws on variable annuity pricing, where a fund or fund of funds may provide a guarantee while fees and guarantee costs are deducted from account value. The proposed risk-neutral treatment is to model those deductions like a dividend yield, reflecting that the investor receives a guarantee or other services in exchange.

This is a conceptual analogy rather than a full pricing prescription: the response supplies no equations, calibration method, or empirical comparison of alternative models. Its rationale depends on the product context and on treating the benefits received in return for fees as relevant to the risk-neutral valuation. It does not establish that fees should always be modeled as dividends for every fund derivative, and it leaves the broader question open for other approaches.

Key ideas

  • A fund’s management fees reduce its account value relative to the assets it holds.
  • In variable annuity pricing, fees and guarantee costs may be deducted from the fund account value.
  • One proposed risk-neutral treatment is to represent those deductions as a dividend yield.
  • The analogy is motivated by benefits such as guarantees or services received in return for the deductions.
  • The response offers a context-dependent rationale rather than a complete or universally applicable pricing model.

Tags

Derivatives pricingOptionsMulti-asset
Full text
# How to find a risk-neutral measure for funds with management fee


# How to find a risk-neutral measure for funds with management fee












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.

## Answer by Frido (score 4)

https://quant.stackexchange.com/a/76461

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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