Hedging and Pricing Derivatives Linked to Investment Funds
Summary
The document explores delta and vega hedging, exotic-product risk, and pricing when a derivative references an investment fund. The question highlights practical constraints: fund shares may be difficult or impossible to short, listed options may be unavailable, and a proxy asset may not track the fund’s behavior. It asks whether proxy options can hedge volatility exposure and whether standard equity models can be adapted with a spread for proxy mismatch.
One response says a negative-delta product could be offset by selling a positive-delta product, while another agrees that short-sale constraints can limit the hedge. Both discuss proxy-based vega hedging, with a warning that a manager can change fund volatility by changing holdings; a contractual arrangement could address this risk. The answers characterize exotic hedging as very difficult and describe pricing guidance as uncertain: suggestions include historical-volatility calibration and models that bound volatility between minimum and maximum levels. These are brief views, not a validated pricing framework or complete hedge design.
Key ideas
- Delta exposure may be offset by selling a positive-delta product, though short-sale constraints can complicate hedging.
- Listed options on a proxy may help hedge vega when fund options are unavailable.
- A fund manager’s ability to change holdings can make proxy volatility hedges unreliable.
- Exotic products on funds are described as difficult to hedge.
- Historical volatility and bounded uncertain-volatility approaches are suggested, without a settled model.
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Full text
# Pricing and hedging fund-linked derivatives # 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? Many thanks in advance for your help ## Answer by dm63 (score 4, accepted) https://quant.stackexchange.com/a/40526 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. ## Answer by user35722 (score 1) https://quant.stackexchange.com/a/41620 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
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