This topic has been raised multiply times already, but I still haven't found a satisfying solution! The problem is:Consider a basket to be a weighted average of underlying assets with fixed weights. Given the implied volatility surfaces of the assets and a fixed correlation matrix, how can we approximate the implied volatility surface for the basket without resorting to monte carlo?I've read several papers on this. One is "Reconstruction of volatility: ....." by Avellaneda and others. But I think they're underestimating the volatility level because they seem to using the volatility of weight geometric average as an approximation. That's why in their imp.vol plots the model vol is much closer to bid vol than ask vol. The other ones are usually MC related, or talks about local correlation, which I'm ignoring at this moment.The question is simply to back out a imp. vol surface for the basket that would match that by MC. Thanks!

There is a paper by Peter Lee, Limin Wang and Karim Abdelkerim in 2003 December issue of Risk Magazine where they do moment matching technique with local correlation model to back out basket skew.