$\alpha$-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
Received: 2021-08-12
Revised :
Accepted: 2021-10-11
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