Ito-Wentzell Formula and Dupire Stochastic PDE

2026/07/14 by Vladimir Lucic · 1 voice · 1 citation
Economics, Econometrics and Finance · Mathematics · #q-fin.MF #math.PR

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arxiv published 2026/07/14 · arxiv updated 2026/07/15

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.

Discussions

• Vladimir Lucic: Ito-Wentzell Formula and Dupire Stochastic PDE https://arxiv.org/abs/2607.12479 https://arxiv.org/pdf/2607.12479 https://arxiv.org/html/2607.12479 [bsky, 0 points, 0 comments]

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