Smile-consistent basket skew
An analytic approximation for the implied volatility surface of basket options is introduced
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Dan Pirjol presents an analytical approximation for the at-the-money (ATM) skew of an option on a basket of assets following correlated local volatility models, which becomes exact in the short-maturity limit. The result is extracted from the short-maturity asymptotic of Avellaneda, Boyer-Olson, Busca and Friz for basket options, and it expresses the basket skew in terms of the ATM volatility levels and skews of the basket components as well as their correlation
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