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!