A Rough-Path PDE Representation for Local Stochastic Volatility

The paper develops a rough-PDE representation for local stochastic volatility models, writing option values as solutions of PDEs driven by a rough-path lift of the volatility-driving noise, with a Feynman–Kac correspondence under rough-path integration. We read it as a way to handle LSV calibration and pricing within rough-path analysis rather than via Monte Carlo alone.

The value satisfies a linear rough PDE dV = ℒV dt + ΓV d𝐖_t interpreted in the rough-path sense, with 𝐖 the lift of the driving noise; Feynman–Kac holds against the rough driver.

The result extends the analytic toolkit — not just simulation — to the LSV models desks actually use for skew, and does so within the rough-path framework that organizes the rest of this literature. It connects local-volatility practice to rough analysis.

Offers an analytic cross-check on LSV Monte Carlo for skew-sensitive memo inputs; consistency between the rough PDE and simulated prices is a usable validation step.

Rough-path solution theory is technically demanding and the regularity conditions constrain admissible coefficients; practical solvers are still maturing.