# Pricing and hedging fund-linked derivatives

I am looking for info regarding pricing, and hedging (notably vega and delta) of derivatives on funds.

Could you please confirm/complete the below information I believe I've understood so far, or guide me to books/papers that could be of any help?

1- Delta hedging: since it is impossible to short funds, any derivatives sold on funds cannot be delta negative (otherwise, issuer is delta positive and would need to short) - is this true?

2- Vega hedging: no options on funds, so the only solution is to find a proxy for which listed options exist and use options on that proxy to try and hedge the vega exposure of the fund derivative. Is there any other way to proceed?

3- Exotic options/structured products: how would you hedge an exotic option on funds, let alone a structured product (ex Autocalls) on funds?

4- Pricing: are there specific pricing models favored for those types of underlying? If not, and using standard equity models such as Heston, would you price the derivative on the proxy and add some sort of spread to account for the fact that the proxy does not behave exactly like the underlying fund?

For Q1 in order to create a negative delta product you would have to offset it by selling a positive delta product to someone else, which is certainly possible.

Q2 I agree with the proxy solution , but it is not very reliable since the fund manager can change the volatility of the fund by changing the composition of the assets. This cannot be avoided unless you have some sort of contractual arrangement with the manager.

Q3 this would be very difficult

Q4 I'm not aware of any specific models. The uncertainty in the distribution would seem to make precise modeling unwarranted.

• To add on @dm63 answer, regarding Q1, most funds charge management fees/operating expanses/etc. that are taken out of the fund value so that the risk neutral drift has to be adjusted accordingly when pricing derivatives. For instance for a fund that makes no income distribution and charges total fees of $1\%$ per annum, the risk neutral drift would be $\text{risk free rate} - 1\%$ – Antoine Conze Jun 27 '18 at 11:36
• Thank you both. Regarding Q2, if vega hedging using a proxy is too approximate, would it be another possibility to do the same "risk recycling" as in Q1 i.e. sell another product with opposite vega to offset it? Do you know which method is preferred in practice? – Alex Jun 27 '18 at 14:58

Q1: Correct.

Q2: There are some variance / volatility swaps quoted in the IDB markets for major mutual funds. Some big hedge funds are also keen to sell volatility.

Q3: Almost impossible.

Q4: Calibration with historical volatility. Eventually with Avenalleda model (uncertain volatility) where you define a min/max vol

Cheers