{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:FFIKCNPJ3AZFYBCU5IXVPH2DBJ","short_pith_number":"pith:FFIKCNPJ","schema_version":"1.0","canonical_sha256":"2950a135e9d8325c0454ea2f579f430a5929a88effdbf50a310baeef4b6b5c2c","source":{"kind":"arxiv","id":"1810.04623","version":1},"attestation_state":"computed","paper":{"title":"Challenges in approximating the Black and Scholes call formula with hyperbolic tangents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.GN","authors_text":"Giovanni Taglialatela, Giuseppe Orlando, Michele Mininni","submitted_at":"2018-09-20T11:11:18Z","abstract_excerpt":"In this paper we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. This formula is useful for pricing and risk management as well as for extracting the implied volatility from quoted options. The latter is of particular importance since it indicates the risk of the underlying and it is the main component of the option's price. Further we estimate numerically the approximating error of the suggested solution and, by comparing our results in computing the implied volatility with th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.04623","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2018-09-20T11:11:18Z","cross_cats_sorted":[],"title_canon_sha256":"462a1de5173169ab4097c79524ca0a7cdc727d6e906d3a88295755df7bcbe2fd","abstract_canon_sha256":"fe8e22a87908cbc72b409917a77dfb8ed585913fb4706a94f791737eaac25515"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:39.581117Z","signature_b64":"YTWZ71fvLEXsuexWZiupWB5t0uyDSbHU3qQ+qnITLqD++ePKCwDdhVdzkqL+vtPI3sX8azuHthKDSgBX4k2ZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2950a135e9d8325c0454ea2f579f430a5929a88effdbf50a310baeef4b6b5c2c","last_reissued_at":"2026-05-18T00:03:39.580467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:39.580467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Challenges in approximating the Black and Scholes call formula with hyperbolic tangents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.GN","authors_text":"Giovanni Taglialatela, Giuseppe Orlando, Michele Mininni","submitted_at":"2018-09-20T11:11:18Z","abstract_excerpt":"In this paper we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. This formula is useful for pricing and risk management as well as for extracting the implied volatility from quoted options. The latter is of particular importance since it indicates the risk of the underlying and it is the main component of the option's price. Further we estimate numerically the approximating error of the suggested solution and, by comparing our results in computing the implied volatility with th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04623","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.04623","created_at":"2026-05-18T00:03:39.580563+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.04623v1","created_at":"2026-05-18T00:03:39.580563+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04623","created_at":"2026-05-18T00:03:39.580563+00:00"},{"alias_kind":"pith_short_12","alias_value":"FFIKCNPJ3AZF","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"FFIKCNPJ3AZFYBCU","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"FFIKCNPJ","created_at":"2026-05-18T12:32:22.470017+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FFIKCNPJ3AZFYBCU5IXVPH2DBJ","json":"https://pith.science/pith/FFIKCNPJ3AZFYBCU5IXVPH2DBJ.json","graph_json":"https://pith.science/api/pith-number/FFIKCNPJ3AZFYBCU5IXVPH2DBJ/graph.json","events_json":"https://pith.science/api/pith-number/FFIKCNPJ3AZFYBCU5IXVPH2DBJ/events.json","paper":"https://pith.science/paper/FFIKCNPJ"},"agent_actions":{"view_html":"https://pith.science/pith/FFIKCNPJ3AZFYBCU5IXVPH2DBJ","download_json":"https://pith.science/pith/FFIKCNPJ3AZFYBCU5IXVPH2DBJ.json","view_paper":"https://pith.science/paper/FFIKCNPJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.04623&json=true","fetch_graph":"https://pith.science/api/pith-number/FFIKCNPJ3AZFYBCU5IXVPH2DBJ/graph.json","fetch_events":"https://pith.science/api/pith-number/FFIKCNPJ3AZFYBCU5IXVPH2DBJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FFIKCNPJ3AZFYBCU5IXVPH2DBJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FFIKCNPJ3AZFYBCU5IXVPH2DBJ/action/storage_attestation","attest_author":"https://pith.science/pith/FFIKCNPJ3AZFYBCU5IXVPH2DBJ/action/author_attestation","sign_citation":"https://pith.science/pith/FFIKCNPJ3AZFYBCU5IXVPH2DBJ/action/citation_signature","submit_replication":"https://pith.science/pith/FFIKCNPJ3AZFYBCU5IXVPH2DBJ/action/replication_record"}},"created_at":"2026-05-18T00:03:39.580563+00:00","updated_at":"2026-05-18T00:03:39.580563+00:00"}