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Reaction-boundary variance and adjoint-consistent local-volatility projection

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  • Chris Angstmann
  • Tim Gebbie

Abstract

We derive an operational-time variance kernel for a latent-order-book reaction boundary and use it to separate three objects usually collapsed in calendar-time volatility models: a structural boundary cumulant, a clock projection, and a pricing-measure choice. The reaction boundary is the zero of a bid--ask imbalance field. For a locally linear book, signed order-flow perturbations displace this zero through a damped Abel response kernel, so the variance of boundary increments is obtained as a finite-scale Green-function cumulant rather than introduced as a primitive diffusion coefficient. For long-memory forcing with exponent $0

Suggested Citation

  • Chris Angstmann & Tim Gebbie, 2026. "Reaction-boundary variance and adjoint-consistent local-volatility projection," Papers 2607.05011, arXiv.org, revised Jul 2026.
    • Handle: RePEc:arx:papers:2607.05011
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    References listed on IDEAS

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