{"paper":{"title":"Affine Option Pricing with Hawkes-Type Endogenous Jump Activity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Shenglan Yuan, Ziyang Fang","submitted_at":"2026-06-26T16:23:41Z","abstract_excerpt":"We develop a risk-neutral option-pricing model where the activity scale of an infinite-activity jump process is endogenously driven by the asset's own realized price jumps. Jump sizes are governed by a normalized asymmetric tempered-stable L\\'evy shape, while a predictable activity scale controls the overall jump intensity and is normalized to coincide with the local jump-induced quadratic-variation rate. Endogenous feedback is introduced through the bounded excitation function $g(y)=1-e^{-ay^2}$, so that small realized jumps excite future activity approximately in proportion to squared jump s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28238","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/2606.28238/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"}