Basket Options, Component Prices, and Dispersion Arbitrage
Summary
The document considers whether a closed-form basket option formula could return each constituent asset’s terminal price, allowing users to evaluate many exotic payoffs from one expression. The response distinguishes that goal from pricing a single basket payoff: a basket price aggregates components, while component-level terminal outcomes require modeling the individual assets and their dependence.
It points to dispersion trading as an options-market approach to relative pricing between a portfolio and its components, and mentions ETF arbitrage as a related setting. The response describes a practical route of pricing the underlying components and then combining them into a basket while accounting for effects such as correlation. It does not present a derivation, formula, or empirical evidence, and the answer explicitly does not establish whether a closed-form component-wise solution exists. Its main value is clarifying the distinction between basket valuation and joint modeling of constituent outcomes.
Key ideas
- A basket option formula typically values an aggregate payoff rather than returning each constituent’s terminal price.
- Component-level outcomes require modeling the assets individually and accounting for their dependence.
- Dispersion trading seeks opportunities in relative pricing between index or portfolio options and component options.
- The response mentions brute-force component pricing as a practical alternative but provides no formal method or evidence.
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Full text
# Has anyone ever derived an analytical basket option which gives terminal asset prices individually, by asset? # Has anyone ever derived an analytical basket option which gives terminal asset prices individually, by asset? Random thought I had around what would be an ideal analytical basket formula. If the formula gave terminal prices of each asset instead of a single basket price, you could price any number of exotic payoffs. Which would in theory make it (nearly) as useful as MC. Could you emulate the same with closed-form solutions that are already published? A creative way to back-solve for each underlying price at expiration? Let's for the sake of keeping things simple assume GBM, or ABM if that would be easier. Note that my question is rather than a closed-form solution for a single basket value, a closed-form solution that provides the terminal values (prices) at expiration OF EACH ASSET IN THE BASKET. If that's possible or not I do not know. ## Answer by AlRacoon (score 2) https://quant.stackexchange.com/a/70584 There are people that attempt to arbitrage the mispricing between portfolio vs components. In options, one method is dispersion. There are other markets where this happens as well such as ETF arbitrage. I don’t know if anyone has a closed form solution to gauge this mispricing as much as they use brute force to price all of the underlying components of the portfolio. And then construct the basket with the individual components, taking into account portfolio effects such as correlation etc., to arrive at the basket prices.
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