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 ?

• I think the better question is : How to extract the basket implied volatility surface? Below a paper I find very easy to comprehend and useful to start with.
– Matt
Dec 21 '12 at 6:11

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

• nice pdfs! can you let me know where the derivation for this comes from?: S(P, Q ) = EQ (ln Q − ln P) Dec 22 '12 at 0:58
• Implicit in those well-chosen PDFs is the point that cointegration matters a lot for baskets. That is to say, the volatility of a basket cannot be inferred from the dynamics of its components alone. The very minimum you can work with is a set of volatilities and a "constant" correlation matrix with the same value $\rho$ for all off-diagonal elements. But the PDFs are more advanced. Dec 22 '12 at 20:36
• @Brian B, good points made. And yes, a constant correlation matrix is the absolute minimum to extract the basket implied vol.
– Matt
Dec 23 '12 at 6:06
• @Nikos, sorry but which part are you referring to?
– Matt
Dec 23 '12 at 6:09
• @Freddy page 59 of your first pdf Dec 28 '12 at 12:55