Reaction-boundary variance and adjoint-consistent local-volatility projection
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摘要
We derive an operational-time variance kernel for a latent-order-book reaction boundary and show how calendar-time local volatility can be obtained via clock projection and pricing-measure choice. The boundary displacement arises from a damped Abel response to signed order-flow, with the variance realized as a finite-scale cumulant rather than a primitive diffusion coefficient. A deterministic activity clock yields a benchmark projection, while non-unique clocks move incompleteness to the projection layer; adjoint consistency provides a reality constraint ensuring coherent pricing across calendar time [page::1].
