Abstract

Public option surfaces can be calibrated without determining the latent risk-neutral coordinates that move non-public stress claims. This paper treats the option manifold as the public image of a latent Volterra-Perron stress state and formulates recovery as a quotient problem. The canonical state contains a directed Volterra contagion operator, a rough maturity-scaling state, a Perron spectral triple, and a synchronized stress coordinate; a residual-density selector is appended only after recovery. The main theorem identifies the public-observable quotient. A Volterra-Perron source state is locally recoverable, up to canonical gauges, exactly when its source quotient embeds into that public quotient, and stable recovery is governed by the quotient observability modulus. Without source-family restrictions, public-equivalent density families preserve the full public option manifold while moving latent-stress claims. Complete pricing and hedgeability require separate payoff-module and tradeable-span conditions. The paper derives martingale drift restrictions, phase-transition charges, native Greeks for recovered state coordinates, a synchronization relative-value identity, and a finite Bachelier-Volterra-Perron benchmark with explicit pricing and hedge residuals.

Citation

Vidal Llauradó, Joan. “Volterra-Perron Pricing of the Option Manifold.” 2026. doi:10.2139/ssrn.6744119