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In this article we propose a $\alpha$-hypergeometric model with uncertainvolatility (UV) where we derive a worst-case scenario for option pricing. Theapproach is based on the connexion between a certain class of nonlinear partialdifferential equations of HJB-type (G-HJB equations), that govern the nonlinearexpectation of the UV model and that provide an alternative to the difficultmodel calibration problem of UV models, and second-order backward stochasticdifferential equations (2BSDEs). Using asymptotic analysis for the G-HJBequation and the equivalent 2BSDE representation, we derive a limit model thatprovides an accurate description of the worst-case price scenario in cases whenthe bounds of the UV model are slowly varying. The analytical results aretested by numerical simulations using a deep learning based approximation ofthe underlying 2BSDE.

$\alpha$-Hypergeometric Uncertain Volatility Models and their Connection to 2BSDEs