{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ALJXGDA6P6YOCVSXIKOVJFNIQQ","short_pith_number":"pith:ALJXGDA6","canonical_record":{"source":{"id":"1507.02847","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2015-07-10T11:03:17Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"8ba13d0963ade9edbc6b9ef813000c6c3e1460378718cb7bc3843dff360b1d83","abstract_canon_sha256":"dc8446a6a0783719ed78edc428aa35e9cf3204777ade4c3f44a40c645ab372c4"},"schema_version":"1.0"},"canonical_sha256":"02d3730c1e7fb0e15657429d5495a8841f2f143c1d6c6b90b115bd3b651ac4c4","source":{"kind":"arxiv","id":"1507.02847","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02847","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02847v2","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02847","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"pith_short_12","alias_value":"ALJXGDA6P6YO","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ALJXGDA6P6YOCVSX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ALJXGDA6","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ALJXGDA6P6YOCVSXIKOVJFNIQQ","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02847","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2015-07-10T11:03:17Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"8ba13d0963ade9edbc6b9ef813000c6c3e1460378718cb7bc3843dff360b1d83","abstract_canon_sha256":"dc8446a6a0783719ed78edc428aa35e9cf3204777ade4c3f44a40c645ab372c4"},"schema_version":"1.0"},"canonical_sha256":"02d3730c1e7fb0e15657429d5495a8841f2f143c1d6c6b90b115bd3b651ac4c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:09.156892Z","signature_b64":"hmLnLKAHV2a9GDN+C8MJ2ALpzANo/9XeSx4m1FmsKeuhGDX630DR5ewqx1yet76bh/wq5aF6fEHiiI6jhulLAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02d3730c1e7fb0e15657429d5495a8841f2f143c1d6c6b90b115bd3b651ac4c4","last_reissued_at":"2026-05-17T23:42:09.156244Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:09.156244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02847","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zAkC80yRLyqcUtTF112NjSy9ReLptkGsqrVqfVgOJqio9X/NJamcQ1tq2u+XpGMwcBC94Q1gvfHDScWUyHuPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:47:13.903570Z"},"content_sha256":"15aed5568ea0da16af3cec4096103db2394186ff5f6b88f9611d7ce0982d8193","schema_version":"1.0","event_id":"sha256:15aed5568ea0da16af3cec4096103db2394186ff5f6b88f9611d7ce0982d8193"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ALJXGDA6P6YOCVSXIKOVJFNIQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Switching to non-affine stochastic volatility: A closed-form expansion for the Inverse Gamma model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.PR"],"primary_cat":"q-fin.CP","authors_text":"Geoffrey Lee, Nicolas Langren\\'e, Zili Zhu","submitted_at":"2015-07-10T11:03:17Z","abstract_excerpt":"This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics $dV_{t}=\\kappa_{t}\\left(\\theta_{t}-V_{t}\\right)dt+\\lambda_{t}V_{t}dB_{t}$. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility model, even though both are as parsimonious (only four stochastic parameters). Indeed, it provides more realistic volatility distribution and volatility paths, which translate in practice into more robust calibration and better hedging accuracy, explaining its popularity "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02847","kind":"arxiv","version":2},"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":"2026-05-17T23:42:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJicdZE+rX9k1B12lhtJkFduC5oY64QPYA2ob196NtODxNsM9Qw1je/q8PZG7HFg3L4nTNhusOVG+NejjeltCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:47:13.903930Z"},"content_sha256":"e3516cb06025349e6f55b93a0bbf582cd9105ba047ef9ea5557c849575e6b670","schema_version":"1.0","event_id":"sha256:e3516cb06025349e6f55b93a0bbf582cd9105ba047ef9ea5557c849575e6b670"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ALJXGDA6P6YOCVSXIKOVJFNIQQ/bundle.json","state_url":"https://pith.science/pith/ALJXGDA6P6YOCVSXIKOVJFNIQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ALJXGDA6P6YOCVSXIKOVJFNIQQ/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":"2026-06-24T05:47:13Z","links":{"resolver":"https://pith.science/pith/ALJXGDA6P6YOCVSXIKOVJFNIQQ","bundle":"https://pith.science/pith/ALJXGDA6P6YOCVSXIKOVJFNIQQ/bundle.json","state":"https://pith.science/pith/ALJXGDA6P6YOCVSXIKOVJFNIQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ALJXGDA6P6YOCVSXIKOVJFNIQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ALJXGDA6P6YOCVSXIKOVJFNIQQ","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":"dc8446a6a0783719ed78edc428aa35e9cf3204777ade4c3f44a40c645ab372c4","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2015-07-10T11:03:17Z","title_canon_sha256":"8ba13d0963ade9edbc6b9ef813000c6c3e1460378718cb7bc3843dff360b1d83"},"schema_version":"1.0","source":{"id":"1507.02847","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02847","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02847v2","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02847","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"pith_short_12","alias_value":"ALJXGDA6P6YO","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ALJXGDA6P6YOCVSX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ALJXGDA6","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:e3516cb06025349e6f55b93a0bbf582cd9105ba047ef9ea5557c849575e6b670","target":"graph","created_at":"2026-05-17T23:42:09Z","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":"This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics $dV_{t}=\\kappa_{t}\\left(\\theta_{t}-V_{t}\\right)dt+\\lambda_{t}V_{t}dB_{t}$. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility model, even though both are as parsimonious (only four stochastic parameters). Indeed, it provides more realistic volatility distribution and volatility paths, which translate in practice into more robust calibration and better hedging accuracy, explaining its popularity ","authors_text":"Geoffrey Lee, Nicolas Langren\\'e, Zili Zhu","cross_cats":["q-fin.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2015-07-10T11:03:17Z","title":"Switching to non-affine stochastic volatility: A closed-form expansion for the Inverse Gamma model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02847","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":"sha256:15aed5568ea0da16af3cec4096103db2394186ff5f6b88f9611d7ce0982d8193","target":"record","created_at":"2026-05-17T23:42:09Z","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":"dc8446a6a0783719ed78edc428aa35e9cf3204777ade4c3f44a40c645ab372c4","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2015-07-10T11:03:17Z","title_canon_sha256":"8ba13d0963ade9edbc6b9ef813000c6c3e1460378718cb7bc3843dff360b1d83"},"schema_version":"1.0","source":{"id":"1507.02847","kind":"arxiv","version":2}},"canonical_sha256":"02d3730c1e7fb0e15657429d5495a8841f2f143c1d6c6b90b115bd3b651ac4c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02d3730c1e7fb0e15657429d5495a8841f2f143c1d6c6b90b115bd3b651ac4c4","first_computed_at":"2026-05-17T23:42:09.156244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:09.156244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hmLnLKAHV2a9GDN+C8MJ2ALpzANo/9XeSx4m1FmsKeuhGDX630DR5ewqx1yet76bh/wq5aF6fEHiiI6jhulLAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:09.156892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02847","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15aed5568ea0da16af3cec4096103db2394186ff5f6b88f9611d7ce0982d8193","sha256:e3516cb06025349e6f55b93a0bbf582cd9105ba047ef9ea5557c849575e6b670"],"state_sha256":"10510a648a5e9339a44ecb37cdaf684ca2fce800d79bc4a7c13ef53a05d6dc0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xehKW38p+5MqSdkFYOcXX8lwFRmjRZMvgMqgkABmJFgmXsXLKnJdNTCqfXpVHIS0haKjZP+zfEzIhPwvmP0+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:47:13.905953Z","bundle_sha256":"999fe59e550b62226a0166a22bbcd0ec46c8a2d2573a979ab73ce173c96424e0"}}