{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:GGP6EHTCY4OBWO7RFDL6YGPAW5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f27ff123532cc3a87cb8e98c490ca6bb0b7a7adf21e0e1356a9d161e450d6cac","cross_cats_sorted":["q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-11-20T11:32:48Z","title_canon_sha256":"570d1e374973f454022edaafd8ff5505d04b55d7384687bf13fecc4bbae19795"},"schema_version":"1.0","source":{"id":"2211.10953","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.10953","created_at":"2026-07-05T06:40:12Z"},{"alias_kind":"arxiv_version","alias_value":"2211.10953v2","created_at":"2026-07-05T06:40:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.10953","created_at":"2026-07-05T06:40:12Z"},{"alias_kind":"pith_short_12","alias_value":"GGP6EHTCY4OB","created_at":"2026-07-05T06:40:12Z"},{"alias_kind":"pith_short_16","alias_value":"GGP6EHTCY4OBWO7R","created_at":"2026-07-05T06:40:12Z"},{"alias_kind":"pith_short_8","alias_value":"GGP6EHTC","created_at":"2026-07-05T06:40:12Z"}],"graph_snapshots":[{"event_id":"sha256:25026d0d9f48d35fd8419ece26184603864e3fda4b4509575d11ef691ee80bd7","target":"graph","created_at":"2026-07-05T06:40:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2211.10953/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies how to price and hedge options under stock models given as a path-dependent SDE solution. When the path-dependent SDE coefficients have Fr\\'{e}chet derivatives, an option price is differentiable with respect to time and the path, and is given as a solution to the path-dependent PDE. This can be regarded as a path-dependent version of the Feynman-Kac formula. As a byproduct, we obtain the differentiability of path-dependent SDE solutions and the SDE representation of their derivatives. In addition, we provide formulas for Greeks with path-dependent coefficient perturbations. ","authors_text":"Hyungbin Park, Kiseop Lee, Seongje Lim","cross_cats":["q-fin.MF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-11-20T11:32:48Z","title":"Option pricing under path-dependent stock models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.10953","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1325672ceeb0a020576fe729362cb8052fbb3b5d0fc7f789c4e19a2dd1ddeb51","target":"record","created_at":"2026-07-05T06:40:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f27ff123532cc3a87cb8e98c490ca6bb0b7a7adf21e0e1356a9d161e450d6cac","cross_cats_sorted":["q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-11-20T11:32:48Z","title_canon_sha256":"570d1e374973f454022edaafd8ff5505d04b55d7384687bf13fecc4bbae19795"},"schema_version":"1.0","source":{"id":"2211.10953","kind":"arxiv","version":2}},"canonical_sha256":"319fe21e62c71c1b3bf128d7ec19e0b77ea4478a126ba57f78d7d6c90773470b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"319fe21e62c71c1b3bf128d7ec19e0b77ea4478a126ba57f78d7d6c90773470b","first_computed_at":"2026-07-05T06:40:12.089504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:40:12.089504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VVtmSpvsuHjy+oVh3UMqE86h9oyIwOaSiKgBu3rPRfjfbRPIIRkXASPWO5O7PetZwHuvP8qXlopu8yC2gbu9CA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:40:12.089980Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.10953","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1325672ceeb0a020576fe729362cb8052fbb3b5d0fc7f789c4e19a2dd1ddeb51","sha256:25026d0d9f48d35fd8419ece26184603864e3fda4b4509575d11ef691ee80bd7"],"state_sha256":"87a42bef058bf9f6d0b4ba91bd3a1bea0bad0ff3b883a53f0dc3dc25d31fd439"}