{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:J22IUHHC5B6LPK4KPUT5X6CC74","short_pith_number":"pith:J22IUHHC","canonical_record":{"source":{"id":"1411.3618","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2014-11-13T17:24:40Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"49a08718987cb9b9f1059ec500f4e67b316776789ab923e5073675ef0d647a31","abstract_canon_sha256":"36ab45480ecaa11af0466303fd66722629b9036981e78e9ef271773af50e4c57"},"schema_version":"1.0"},"canonical_sha256":"4eb48a1ce2e87cb7ab8a7d27dbf842ff1a06a68d5ddd4383226303f6582716c5","source":{"kind":"arxiv","id":"1411.3618","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3618","created_at":"2026-05-18T01:04:33Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3618v5","created_at":"2026-05-18T01:04:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3618","created_at":"2026-05-18T01:04:33Z"},{"alias_kind":"pith_short_12","alias_value":"J22IUHHC5B6L","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J22IUHHC5B6LPK4K","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J22IUHHC","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:J22IUHHC5B6LPK4KPUT5X6CC74","target":"record","payload":{"canonical_record":{"source":{"id":"1411.3618","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2014-11-13T17:24:40Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"49a08718987cb9b9f1059ec500f4e67b316776789ab923e5073675ef0d647a31","abstract_canon_sha256":"36ab45480ecaa11af0466303fd66722629b9036981e78e9ef271773af50e4c57"},"schema_version":"1.0"},"canonical_sha256":"4eb48a1ce2e87cb7ab8a7d27dbf842ff1a06a68d5ddd4383226303f6582716c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:33.513099Z","signature_b64":"c7QLgvuS4k5odGxuHOoE6YZQwXWSNqfq8OmnJbHkdvz9yzElLh76tkPcjGFSRaQCKc4IA0KfjWeeId5W8p51Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4eb48a1ce2e87cb7ab8a7d27dbf842ff1a06a68d5ddd4383226303f6582716c5","last_reissued_at":"2026-05-18T01:04:33.512359Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:33.512359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.3618","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eyYB02+8ilNUmuESNxK8DNI+E0jLGcR45nyDxCCFcF5l17kN7x1vtv9EHdOdpSoXbewNqztAqijdA3ciwXNuCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T04:31:19.024049Z"},"content_sha256":"7fbdad0d0c04563ba25fe4c826586adde11d0d37086ab7e7ad29b087274f0546","schema_version":"1.0","event_id":"sha256:7fbdad0d0c04563ba25fe4c826586adde11d0d37086ab7e7ad29b087274f0546"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:J22IUHHC5B6LPK4KPUT5X6CC74","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Forward Equation for Barrier Options under the Brunick&Shreve Markovian Projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.MF","authors_text":"Ben Hambly, Christoph Reisinger, Matthieu Mariapragassam","submitted_at":"2014-11-13T17:24:40Z","abstract_excerpt":"We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient derived by Brunick and Shreve for their mimicking diffusion and can be interpreted as the canonical extension of local volatility for barrier options. Alternatively, a forward partial-integro differential equation (PIDE) is introduced which provides up-and-out call prices, under a Brunick-Shreve model, for the complete set of strikes, barriers and maturities in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3618","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A7yqOFL78dasnOrB725E/X2ADCTYu3RzYCTC+hzJz9i7juGSrgDlIT4uXiaPrbpKlZilTDavtWiIEH6VsTdgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T04:31:19.024735Z"},"content_sha256":"730fd1e7548471ea68446e7430930a005f90f3f346ec1debb7653b3e3da4cd29","schema_version":"1.0","event_id":"sha256:730fd1e7548471ea68446e7430930a005f90f3f346ec1debb7653b3e3da4cd29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J22IUHHC5B6LPK4KPUT5X6CC74/bundle.json","state_url":"https://pith.science/pith/J22IUHHC5B6LPK4KPUT5X6CC74/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J22IUHHC5B6LPK4KPUT5X6CC74/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-20T04:31:19Z","links":{"resolver":"https://pith.science/pith/J22IUHHC5B6LPK4KPUT5X6CC74","bundle":"https://pith.science/pith/J22IUHHC5B6LPK4KPUT5X6CC74/bundle.json","state":"https://pith.science/pith/J22IUHHC5B6LPK4KPUT5X6CC74/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J22IUHHC5B6LPK4KPUT5X6CC74/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:J22IUHHC5B6LPK4KPUT5X6CC74","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":"36ab45480ecaa11af0466303fd66722629b9036981e78e9ef271773af50e4c57","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2014-11-13T17:24:40Z","title_canon_sha256":"49a08718987cb9b9f1059ec500f4e67b316776789ab923e5073675ef0d647a31"},"schema_version":"1.0","source":{"id":"1411.3618","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3618","created_at":"2026-05-18T01:04:33Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3618v5","created_at":"2026-05-18T01:04:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3618","created_at":"2026-05-18T01:04:33Z"},{"alias_kind":"pith_short_12","alias_value":"J22IUHHC5B6L","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J22IUHHC5B6LPK4K","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J22IUHHC","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:730fd1e7548471ea68446e7430930a005f90f3f346ec1debb7653b3e3da4cd29","target":"graph","created_at":"2026-05-18T01:04:33Z","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"},"paper":{"abstract_excerpt":"We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient derived by Brunick and Shreve for their mimicking diffusion and can be interpreted as the canonical extension of local volatility for barrier options. Alternatively, a forward partial-integro differential equation (PIDE) is introduced which provides up-and-out call prices, under a Brunick-Shreve model, for the complete set of strikes, barriers and maturities in","authors_text":"Ben Hambly, Christoph Reisinger, Matthieu Mariapragassam","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2014-11-13T17:24:40Z","title":"A Forward Equation for Barrier Options under the Brunick&Shreve Markovian Projection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3618","kind":"arxiv","version":5},"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":"sha256:7fbdad0d0c04563ba25fe4c826586adde11d0d37086ab7e7ad29b087274f0546","target":"record","created_at":"2026-05-18T01:04:33Z","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":"36ab45480ecaa11af0466303fd66722629b9036981e78e9ef271773af50e4c57","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2014-11-13T17:24:40Z","title_canon_sha256":"49a08718987cb9b9f1059ec500f4e67b316776789ab923e5073675ef0d647a31"},"schema_version":"1.0","source":{"id":"1411.3618","kind":"arxiv","version":5}},"canonical_sha256":"4eb48a1ce2e87cb7ab8a7d27dbf842ff1a06a68d5ddd4383226303f6582716c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4eb48a1ce2e87cb7ab8a7d27dbf842ff1a06a68d5ddd4383226303f6582716c5","first_computed_at":"2026-05-18T01:04:33.512359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:33.512359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c7QLgvuS4k5odGxuHOoE6YZQwXWSNqfq8OmnJbHkdvz9yzElLh76tkPcjGFSRaQCKc4IA0KfjWeeId5W8p51Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:33.513099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3618","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fbdad0d0c04563ba25fe4c826586adde11d0d37086ab7e7ad29b087274f0546","sha256:730fd1e7548471ea68446e7430930a005f90f3f346ec1debb7653b3e3da4cd29"],"state_sha256":"95426d01920ae21c9ff862a8a1d4abf09953f8dd36d837482ff29b1afdbc1689"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A0Ycfv+BdKy1j61x4S3AFG/aNQkiGTk7WK2Emy8piu4YHcYoVW+KLZZp4/aidw10rMiH7yd4K6+dPZNipfT5Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T04:31:19.028165Z","bundle_sha256":"f608358acaf16c22ad1dc9013720891af6caf0a1c880ced2f7d7bcdbbbd9ebcc"}}