2021 / September Volume 16 No.3
$\alpha$-Hypergeometric Uncertain Volatility Models and their Connection to 2BSDEs
| Published Date |
2021 / September
|
|---|---|
| Title | $\alpha$-Hypergeometric Uncertain Volatility Models and their Connection to 2BSDEs |
| Author | |
| Keyword | |
| Download | |
| Pagination | 263-288 |
| 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.
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| DOI | |
| AMS Subject Classification |
91G30, 35Q93
|
| Received |
2021-08-12
|
| Accepted |
2021-10-11
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