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$\alpha$-Hypergeometric Uncertain Volatility Models and their Connection to 2BSDEs
by Zaineb Mezdoud   Carsten Hartmann   Mohamed Riad Remita   Omar Kebiri

Vol. 16 No. 3 (2021) P.263~P.288
 DOI: https://doi.org/10.21915/BIMAS.2021304 10.21915/BIMAS.2021304

ABSTRACT

In this article we propose a $\alpha$-hypergeometric model with uncertain volatility (UV) where we derive a worst-case scenario for option pricing. The approach is based on the connection between a certain class of nonlinear partial differential equations of HJB-type (G-HJB equations), that governs the nonlinear expectation of the UV model and provides an alternative to the difficult model calibration problem of UV models, and second-order backward stochastic differential equations (2BSDEs). Using asymptotic analysis for the G-HJB equation and the equivalent 2BSDE representation, we derive a limit model which provides an accurate description of the worst-case price scenario in cases when the bounds of the UV model are slowly varying. The analytical results are tested by numerical simulations using a deep learning based approximation of the underlying 2BSDE.

KEYWORDS
α-hypergeometric stochastic volatility model, uncertain volatility model, 2BSDE, deep learning based discretisation of 2BSDE

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 91G30, 35Q93

MILESTONES