Cross-dependent volatility

Julien Guyon introduces cross-dependent volatility models and calibrate them to market smiles

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