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arXiv · 2607.12479

Ito-Wentzell Formula and Dupire Stochastic PDE

Vladimir Lucic
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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.

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Vladimir Lucic. 2026-07-15. Ito-Wentzell Formula and Dupire Stochastic PDE. https://arxiv.org/abs/2607.12479

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