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

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  • Zaineb Mezdoud
  • Carsten Hartmann
  • Mohamed Riad Remita
  • Omar Kebiri

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 connexion between a certain class of nonlinear partial differential equations of HJB-type (G-HJB equations), that govern the nonlinear expectation of the UV model and that provide 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 that 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.

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  • Zaineb Mezdoud & Carsten Hartmann & Mohamed Riad Remita & Omar Kebiri, 2021. "$\alpha$-Hypergeometric Uncertain Volatility Models and their Connection to 2BSDEs," Papers 2108.06965, arXiv.org.
    • Handle: RePEc:arx:papers:2108.06965
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    References listed on IDEAS

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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
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