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Ito-Wentzell Formula and Dupire Stochastic PDE

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  • 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.

Suggested Citation

  • Vladimir Lucic, 2026. "Ito-Wentzell Formula and Dupire Stochastic PDE," Papers 2607.12479, arXiv.org.
    • Handle: RePEc:arx:papers:2607.12479
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    File URL: https://arxiv.org/pdf/2607.12479
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