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Why Basket Option Volatility Requires a Surface and Basket Model

Article Quant Q&A · Author: glyphard
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Summary

The document asks how to combine the individual implied volatilities of several stocks into one volatility for a weighted basket option. The response cautions that a single spot implied volatility for each constituent is insufficient for quoting or valuing basket options. It recommends considering implied volatility surfaces, which capture how implied volatility varies across strikes and maturities, including smile and skew effects.

The response points toward further study but does not provide a formula or calculate a basket volatility from the supplied weights. In practice, basket volatility also depends on the constituents’ correlations and the precise basket and option payoff definitions, so weighting individual implied volatilities alone does not determine the answer. A full valuation requires relevant market data and a model suited to the basket structure.

Key ideas

  • A basket’s implied volatility cannot generally be obtained by simply averaging constituent implied volatilities by their weights.
  • Option pricing requires volatility information across strikes and maturities to account for smile and skew.
  • Basket valuation also depends on relationships among constituent returns, including their correlations.
  • The document offers a direction for further analysis but supplies no calculation method or numerical result.

Tags

OptionsVolatilityDerivatives pricing
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# what is the implied volatility on a basket of options


# what is the implied volatility on a basket of options












If I have 4 optionable stocks A,B,C,D and each different implied volatilies,IV-A,IV-B,IV-C,IV-D. How do get the implied volatility for a basket option on A,B,C,D where the basket weights are w-A=.6, w-B=.3, w-C=.09,w-D=.01 ?

## Answer by Matt Wolf (score 6)

https://quant.stackexchange.com/a/4814

I think you should not just ask what the implied vol is of a basket of equity derivatives but you should aim to generate a volatility surface. A spot implied vol gives you nothing to work with. What you need is an implied vol surface in order to understand the smile and skew effects when you quote basket options in the market and/or as price taker. Take a look at the following to get started:

http://www.wilmott.com/pdfs/100826qu.pdf

http://relativity.phys.lsu.edu/postdocs/matt/papers/sv.pdf

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.