Risk-Neutral Pricing of Put Protection on a Multi-Asset Fund
Summary
The document raises practical questions about valuing put protection on a fund with a strong historical record and relatively stable volatility. It asks whether the fund price can serve as the underlying in a Black–Scholes framework, how to account for management and protection charges deducted from fund value, and how reinvested income affects those deductions. It also points out a feedback loop: a larger premium reduces fund value and may increase the chance that the put finishes in the money. The discussion does not provide a pricing method or resolve these modeling questions.
A reply points readers to research on put-protection strategies and suggests that their performance may be weaker than intuition suggests, with alternative downside hedges worth considering under fund-allocation constraints. The linked research is cited but not summarized or evaluated in the document, so it supplies no evidence, performance figures, or details about the comparison. The fund’s asset mix, contract terms, fee structure, and assumptions about returns and volatility are also unspecified; conclusions about a particular fund or hedge cannot be drawn from the post alone.
Key ideas
- The post asks whether a multi-asset fund's value is an appropriate underlying for pricing a protective put.
- Fees and put premiums deducted from fund value create a feedback between option cost and future fund performance.
- The author asks whether reinvested portfolio income can offset management and protection charges.
- A reply points to research suggesting put-protection strategies may underperform and mentions alternative hedges, without summarizing supporting evidence.
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Full text
# How to price a put option on a multi-asset fund? Confused by risk-neutral pricing implicaton on real world # How to price a put option on a multi-asset fund? Confused by risk-neutral pricing implicaton on real world The fund has super track record with stable vol. The chance for this Put to pay out is very low in real world, but a B/S risk-neutral pricing would give a very high cost. I am struggling with the following: - What is the underlying variable? The fund price? The B/S model would assume there is no difference between this fund and any other assets or funds in the market. - All charges are deducted from the fund itself including annual management fee and the Put protection cost, both as a % of the future fund values which are unknown at time 0. These charges can be input as dividend yields. But in B/S the dividend yield is a % of the spot price. - The premium is both an input and output. It needs to be solved iteratively until it converges into a very large number. It's counterintuitive in real world that the higher the premium (being deducted from the fund) the higher the chance of Put payout at maturity. In other words, the fund needs to outperform the risk free + fund management charge + put premium in order to be breakeven. - The fund receives regular dividend and incomes from various assets like equities, fixed incomes etc. All are reinvested into the fund. Can these incomes/yield be used to offset the deduction of management fees and premium charges? Any suggestions will be highly appreciated. Thanks! ## Answer by Dr. Michael J. Stefano (score 1) https://quant.stackexchange.com/a/85335 this doesnt answer your question directly but brings into consideration the fact the put protection strategies significantly UNDERPERFORM, contrary to what might seem intuitive. lots of good stuff in this pdf that could make for considering a diff strategy for hedging downside depending on limitations on fund monies allocations. https://cdn.cboe.com/resources/education/research_publications/PutWriteCBOE19_v14_by_Prof_Oleg_Bondarenko_as_of_June_14.pdf
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