{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:76TGAWJTQNDBWOXDDZ3FG3MJLX","short_pith_number":"pith:76TGAWJT","canonical_record":{"source":{"id":"2006.01542","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2020-06-02T12:07:44Z","cross_cats_sorted":[],"title_canon_sha256":"a695094f42ca7440a9a83773f700a271dd93f1521640ff266c0533ecade68938","abstract_canon_sha256":"d8c77aa6b6fc8b51568425152303b4d512bcf695295de0d8ff514d3069aa6269"},"schema_version":"1.0"},"canonical_sha256":"ffa660593383461b3ae31e76536d895dc60a0df195bab74e13f17c916907162e","source":{"kind":"arxiv","id":"2006.01542","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.01542","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"2006.01542v7","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.01542","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"76TGAWJTQNDB","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"pith_short_16","alias_value":"76TGAWJTQNDBWOXD","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"pith_short_8","alias_value":"76TGAWJT","created_at":"2026-06-02T02:04:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:76TGAWJTQNDBWOXDDZ3FG3MJLX","target":"record","payload":{"canonical_record":{"source":{"id":"2006.01542","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2020-06-02T12:07:44Z","cross_cats_sorted":[],"title_canon_sha256":"a695094f42ca7440a9a83773f700a271dd93f1521640ff266c0533ecade68938","abstract_canon_sha256":"d8c77aa6b6fc8b51568425152303b4d512bcf695295de0d8ff514d3069aa6269"},"schema_version":"1.0"},"canonical_sha256":"ffa660593383461b3ae31e76536d895dc60a0df195bab74e13f17c916907162e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:44.405299Z","signature_b64":"T5nUbmBtTbGWXw1hmhC8yA2tSMW5tN7iZIUrlsh3X+dP0ufvnSEGXoAlSwlb309aL/VZ0EhOcHM6QpgzHSnRDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffa660593383461b3ae31e76536d895dc60a0df195bab74e13f17c916907162e","last_reissued_at":"2026-06-02T02:04:44.404973Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:44.404973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.01542","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T02:04:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nZjYNg0vraPXe9jCwYl2HequtZHTGXSF5V97UgedtqHjrCt0aswwFgKOl2+zfrIcn20QoXgKFAmzvX82/mXxBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:21:06.660574Z"},"content_sha256":"be9941c38e6706f7239809fa18870b8f3e4936381eae61c7dc0cc27fa361380e","schema_version":"1.0","event_id":"sha256:be9941c38e6706f7239809fa18870b8f3e4936381eae61c7dc0cc27fa361380e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:76TGAWJTQNDBWOXDDZ3FG3MJLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit approximations of option prices via Malliavin calculus in a general stochastic volatility framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.MF","authors_text":"Kaustav Das, Nicolas Langren\\'e","submitted_at":"2020-06-02T12:07:44Z","abstract_excerpt":"We establish an explicit approximation formula for European put option prices within a general stochastic volatility model with time-dependent parameters. Our methodology is based on expansions of the mixing representation of the put option price as an expectation of the Black-Scholes formula, in which the resulting terms are calculated explicitly by Malliavin calculus. We obtain an explicit representation of the error generated by the expansion procedure, and bound it in terms of moments of functionals of the underlying volatility process. Under the assumption of piecewise-constant parameters"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.01542","kind":"arxiv","version":7},"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/2006.01542/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T02:04:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0U3e+/aP9CEOPx0kglOFkW2XjH0D0qFyErMqZkpFtw/PMCgRb11J16v3SsFe43KgST53y3tKcAKhlQir5KGTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:21:06.660951Z"},"content_sha256":"1bf7638f7ad698ad694347170bb8b70d47b8b732c77218f0b2628115f79fb2f4","schema_version":"1.0","event_id":"sha256:1bf7638f7ad698ad694347170bb8b70d47b8b732c77218f0b2628115f79fb2f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/76TGAWJTQNDBWOXDDZ3FG3MJLX/bundle.json","state_url":"https://pith.science/pith/76TGAWJTQNDBWOXDDZ3FG3MJLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/76TGAWJTQNDBWOXDDZ3FG3MJLX/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":"2026-06-22T09:21:06Z","links":{"resolver":"https://pith.science/pith/76TGAWJTQNDBWOXDDZ3FG3MJLX","bundle":"https://pith.science/pith/76TGAWJTQNDBWOXDDZ3FG3MJLX/bundle.json","state":"https://pith.science/pith/76TGAWJTQNDBWOXDDZ3FG3MJLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/76TGAWJTQNDBWOXDDZ3FG3MJLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:76TGAWJTQNDBWOXDDZ3FG3MJLX","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":"d8c77aa6b6fc8b51568425152303b4d512bcf695295de0d8ff514d3069aa6269","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2020-06-02T12:07:44Z","title_canon_sha256":"a695094f42ca7440a9a83773f700a271dd93f1521640ff266c0533ecade68938"},"schema_version":"1.0","source":{"id":"2006.01542","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.01542","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"2006.01542v7","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.01542","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"76TGAWJTQNDB","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"pith_short_16","alias_value":"76TGAWJTQNDBWOXD","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"pith_short_8","alias_value":"76TGAWJT","created_at":"2026-06-02T02:04:44Z"}],"graph_snapshots":[{"event_id":"sha256:1bf7638f7ad698ad694347170bb8b70d47b8b732c77218f0b2628115f79fb2f4","target":"graph","created_at":"2026-06-02T02:04:44Z","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/2006.01542/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish an explicit approximation formula for European put option prices within a general stochastic volatility model with time-dependent parameters. Our methodology is based on expansions of the mixing representation of the put option price as an expectation of the Black-Scholes formula, in which the resulting terms are calculated explicitly by Malliavin calculus. We obtain an explicit representation of the error generated by the expansion procedure, and bound it in terms of moments of functionals of the underlying volatility process. Under the assumption of piecewise-constant parameters","authors_text":"Kaustav Das, Nicolas Langren\\'e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2020-06-02T12:07:44Z","title":"Explicit approximations of option prices via Malliavin calculus in a general stochastic volatility framework"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.01542","kind":"arxiv","version":7},"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:be9941c38e6706f7239809fa18870b8f3e4936381eae61c7dc0cc27fa361380e","target":"record","created_at":"2026-06-02T02:04:44Z","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":"d8c77aa6b6fc8b51568425152303b4d512bcf695295de0d8ff514d3069aa6269","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2020-06-02T12:07:44Z","title_canon_sha256":"a695094f42ca7440a9a83773f700a271dd93f1521640ff266c0533ecade68938"},"schema_version":"1.0","source":{"id":"2006.01542","kind":"arxiv","version":7}},"canonical_sha256":"ffa660593383461b3ae31e76536d895dc60a0df195bab74e13f17c916907162e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffa660593383461b3ae31e76536d895dc60a0df195bab74e13f17c916907162e","first_computed_at":"2026-06-02T02:04:44.404973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:44.404973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T5nUbmBtTbGWXw1hmhC8yA2tSMW5tN7iZIUrlsh3X+dP0ufvnSEGXoAlSwlb309aL/VZ0EhOcHM6QpgzHSnRDw==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:44.405299Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.01542","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be9941c38e6706f7239809fa18870b8f3e4936381eae61c7dc0cc27fa361380e","sha256:1bf7638f7ad698ad694347170bb8b70d47b8b732c77218f0b2628115f79fb2f4"],"state_sha256":"70e5f40b1e058e14d547786ed0a2fcb3beee6fd1e6da9afcb43c882c0fa66622"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O75m4nRCXiIj44N6wQuZrF4Sfehp+AhXiU/jd9gBVIE0XVxRkYRHpBEVpnvnTqrzGbexhzQRmBBKTHtMiUZrCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:21:06.662962Z","bundle_sha256":"3e1ab3998cb506717e0ffa450c1ca889eeb328515a57ae027d84b66ccf5bdd63"}}