Ito-Wentzell Formula and Dupire Stochastic PDE

Vladimir Lucic

Papers from arXiv.org

Abstract: Starting from the classic result of Wentzell, we derive a conditional forward equation and an associated stochastic Dupire PDE for a local-stochastic-volatility model (LSV). As an application, we obtain a density-weighted Rao--Blackwell estimator for the leverage function in LSV. We also derive an SPDE for a rolling expiry vanilla option, in the spirit of the Musiela parametrization in interest rate modeling.

Date: 2026-07, Revised 2026-07
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