{"paper":{"title":"Option prices from operational-time reaction-boundary lattices","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["q-fin.MF","q-fin.TR"],"primary_cat":"q-fin.PR","authors_text":"Chris Angstmann, Tim Gebbie","submitted_at":"2026-06-08T14:38:58Z","abstract_excerpt":"We consider the role of a continuum operational time u and its mapping to calendar time t and how these relate to event time for option pricing problems. We derive option-pricing equations from an operational-time Markov lattice rather than from a calendar-time diffusion. The primitive model is a nearest-neighbour log-price lattice with state- and time-dependent transition probabilities. Its Chapman-Kolmogorov decomposition yields discrete forward and backward equations, which converge under local finite-variance scaling to the usual continuum adjoint pair. In price variables, the backward equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09564","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.09564/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}