Basket Put Options and Delta Hedging for Multi-Asset Portfolios
Summary
The question considers insuring a portfolio of large- and small-cap US equity ETFs against a loss beyond a portfolio-wide threshold. It contrasts a single payoff based on the combined basket with separate options on each holding, which could pay when one component falls sharply even if the overall portfolio remains above the intended protection level.
The answer identifies the desired contract as a basket put and notes that pricing it is nontrivial, recommending comparison of dealer quotes. It also cautions that delta hedging only offsets changes in spot prices; it does not eliminate exposure to volatility or correlation, particularly when practical markets depart from Black–Scholes assumptions. The exchange does not calculate a price, prove that basket protection would be cheaper, or specify a model for the basket’s dynamics, so those points require further analysis.
Key ideas
- A put on the combined portfolio can target a loss threshold for the basket as a whole.
- Separate options on portfolio components may pay even when the aggregate portfolio has not crossed its protection threshold.
- Pricing a multi-asset basket option is complex and depends on the basket’s behavior.
- Delta hedging offsets spot-price movements but leaves volatility and correlation exposure.
Tags
Full text
# How do you price an option on multiple things> # How do you price an option on multiple things> Suppose, for simplicity, I want to cover the U.S. stock market by buying ETFs for the Russell 1000 and Russell 2000. But I want to overweight small cap, so the Russell 3000 won't do. Also, let's assume none of these ETFs has options on it, as I am more interested in the delta hedging practice. Let's also assume I want to protect my whole portfolio against a drop of more than 10%. And I have enough money to be able to go to an investment bank and get a custom-tailored swap to make this happen. Now the obvious and easy thing to do is for them to create two delta hedged portfolios, using the ETFs to get an exact hedge. But that seems like its overly costly to me, because I was only concerned about the total portfolio dropping more than 10%. If they did two portfolios, and the R1000 is down 4% (and is the bigger holding), while the R2000 is down 14%, I'm going to get a payoff on the R2000 option. But my total portfolio was down only maybe 6%, so, in essence, I paid too much for the protection I wanted: I only care if the total portfolio drops more than 10%. Can that be delta-hedged with one portfolio, and if so, how would it be done? And would it indeed be cheaper? ## Answer by user34971 (score 1) https://quant.stackexchange.com/a/50101 - Multiple "things" = Multi-Asset option. Based on your description it seems to me that what you need is a 90% basket put option. Call 3-4 banks and ask them to price it, pick the best price. It's far from trivial to price a basket option. - Delta-hedging does not have the same effect as an option. Rather, it neutralizes moves in the spot prices, but leaves volatility and correlation open, because Black-Scholes assumptions are always going to be violated in practice. I am referring to Black-Scholes because I am not sure whether you are already thinking of (L)SV modelling. See for example this thread for intro to basket options pricing.
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