Ito-Wentzell Formula and Dupire Stochastic PDE

Vladimir Lucic

Ito-Wentzell Formula and Dupire Stochastic PDE

Mathematical Finance 2026-07-14 v1 Probability

Authors: Vladimir Lucic

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.

Keywords

Ito-Wentzell formula Dupire PDE local-stochastic-volatility model leverage function Rao-Blackwell estimator Musiela parametrization

Cite

@article{arxiv.2607.12479,
  title  = {Ito-Wentzell Formula and Dupire Stochastic PDE},
  author = {Vladimir Lucic},
  journal= {arXiv preprint arXiv:2607.12479},
  year   = {2026}
}