Cross-dependent volatility

Local volatilities in multiasset models typically have no cross-asset dependency. Julien Guyon introduces cross-dependent volatility models and explains how to calibrate them to market smiles and how they can be used to assess model risk, capture historical behaviour, and generate steep index skews without correlation skew

The classical model for simultaneously calibrating stocks and index smiles is extremal within the class of CDV models, in the sense that the simplest volatility model calibrating to the N individual smiles is used, and the extra skewness of the index smile results purely from correlation.

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Here, we introduce another model, which is extremal in the opposite direction: the simplest correlation model (state-independent correlation) is imposed, and the extra skewness of the