{"paper":{"title":"Multiplicative Langevin Process for Volatilities Produces Observed Q-Variance Regularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.ST"],"primary_cat":"q-fin.PR","authors_text":"Alex Dannenberg, William H. Press","submitted_at":"2026-05-30T16:37:09Z","abstract_excerpt":"Q-variance (so-called) posits a statistical relationship $\\mathbf{E}(\\sigma^2 | z) = \\sigma_0^2 + \\tfrac{1}{2}z^2$ between an asset's volatility $\\sigma^2$, as observed in a time interval $T$, and its (suitably scaled) return $z$ in the same interval. We here show that this relationship is {\\em exactly equivalent} to to positing an Inverse Gamma probability distribution for $\\sigma^2$ itself. We then show that such a distribution is exactly generated by a multiplicative Langevin process with an arbitrary, settable coherence time $\\tau_c$, so that very nearly the same Q-variance relationship wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00800","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/2606.00800/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"}