{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NZVUIBSP6GWC7DM5DWDTACRBMB","short_pith_number":"pith:NZVUIBSP","canonical_record":{"source":{"id":"1309.2383","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2013-09-10T06:11:11Z","cross_cats_sorted":[],"title_canon_sha256":"f8d85b8d9c8fa44079c29ee8232937ab984eb0dabafc694fb29135344156e608","abstract_canon_sha256":"415f96b6ee3817acbff1f040b074679abdd9974849dd977b90ee9c0c853479e5"},"schema_version":"1.0"},"canonical_sha256":"6e6b44064ff1ac2f8d9d1d87300a21605a61f9ecc5d3364c92b015486f0631a0","source":{"kind":"arxiv","id":"1309.2383","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2383","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2383v1","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2383","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"pith_short_12","alias_value":"NZVUIBSP6GWC","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"NZVUIBSP6GWC7DM5","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"NZVUIBSP","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NZVUIBSP6GWC7DM5DWDTACRBMB","target":"record","payload":{"canonical_record":{"source":{"id":"1309.2383","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2013-09-10T06:11:11Z","cross_cats_sorted":[],"title_canon_sha256":"f8d85b8d9c8fa44079c29ee8232937ab984eb0dabafc694fb29135344156e608","abstract_canon_sha256":"415f96b6ee3817acbff1f040b074679abdd9974849dd977b90ee9c0c853479e5"},"schema_version":"1.0"},"canonical_sha256":"6e6b44064ff1ac2f8d9d1d87300a21605a61f9ecc5d3364c92b015486f0631a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:44.832810Z","signature_b64":"A65ZO850JLoc43AarVjyxzIzdAubzWyzMX6eRpUdRgOz7rWYNP3GtVRlPLS7URijpG0qJeTiEqmxCyfCHlj0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e6b44064ff1ac2f8d9d1d87300a21605a61f9ecc5d3364c92b015486f0631a0","last_reissued_at":"2026-05-18T03:13:44.832174Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:44.832174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.2383","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mQ5XQDUqhBvSRF4yy/YIUaCYQAU9Dfc/MEdIoejMY6lWKOAtizTNtC6+yDEW6fIEaX4H6S+GB9y+8PhdnirYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T23:58:42.344636Z"},"content_sha256":"4bde4e6f6d704ce35c95136b225f0f4550236827684c78c98eb992ef67a5608a","schema_version":"1.0","event_id":"sha256:4bde4e6f6d704ce35c95136b225f0f4550236827684c78c98eb992ef67a5608a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NZVUIBSP6GWC7DM5DWDTACRBMB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On lower and upper bounds for Asian-type options: a unified approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.PR","authors_text":"Alexander Novikov, Nino Kordzakhia","submitted_at":"2013-09-10T06:11:11Z","abstract_excerpt":"In the context of dealing with financial risk management problems it is desirable to have accurate bounds for option prices in situations when pricing formulae do not exist in the closed form. A unified approach for obtaining upper and lower bounds for Asian-type options, including options on VWAP, is proposed in this paper. The bounds obtained are applicable to the continuous and discrete-time frameworks for the case of time-dependent interest rates. Numerical examples are provided to illustrate the accuracy of the bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2383","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ixM06p7naejhgE9cRffZmPm1m3vpEBzxljDKlzJ4pDN8u6KZKcClz0sMIxEfDKCnZcv39DMxt6+DJg9NNbAuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T23:58:42.345289Z"},"content_sha256":"00238e7c1a183ca7ccd62405fd04ce441a57af767c4dbf1035c5d2df48a18719","schema_version":"1.0","event_id":"sha256:00238e7c1a183ca7ccd62405fd04ce441a57af767c4dbf1035c5d2df48a18719"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZVUIBSP6GWC7DM5DWDTACRBMB/bundle.json","state_url":"https://pith.science/pith/NZVUIBSP6GWC7DM5DWDTACRBMB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZVUIBSP6GWC7DM5DWDTACRBMB/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":"2026-05-19T23:58:42Z","links":{"resolver":"https://pith.science/pith/NZVUIBSP6GWC7DM5DWDTACRBMB","bundle":"https://pith.science/pith/NZVUIBSP6GWC7DM5DWDTACRBMB/bundle.json","state":"https://pith.science/pith/NZVUIBSP6GWC7DM5DWDTACRBMB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZVUIBSP6GWC7DM5DWDTACRBMB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NZVUIBSP6GWC7DM5DWDTACRBMB","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":"415f96b6ee3817acbff1f040b074679abdd9974849dd977b90ee9c0c853479e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2013-09-10T06:11:11Z","title_canon_sha256":"f8d85b8d9c8fa44079c29ee8232937ab984eb0dabafc694fb29135344156e608"},"schema_version":"1.0","source":{"id":"1309.2383","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2383","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2383v1","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2383","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"pith_short_12","alias_value":"NZVUIBSP6GWC","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"NZVUIBSP6GWC7DM5","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"NZVUIBSP","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:00238e7c1a183ca7ccd62405fd04ce441a57af767c4dbf1035c5d2df48a18719","target":"graph","created_at":"2026-05-18T03:13:44Z","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"},"paper":{"abstract_excerpt":"In the context of dealing with financial risk management problems it is desirable to have accurate bounds for option prices in situations when pricing formulae do not exist in the closed form. A unified approach for obtaining upper and lower bounds for Asian-type options, including options on VWAP, is proposed in this paper. The bounds obtained are applicable to the continuous and discrete-time frameworks for the case of time-dependent interest rates. Numerical examples are provided to illustrate the accuracy of the bounds.","authors_text":"Alexander Novikov, Nino Kordzakhia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2013-09-10T06:11:11Z","title":"On lower and upper bounds for Asian-type options: a unified approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2383","kind":"arxiv","version":1},"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":"sha256:4bde4e6f6d704ce35c95136b225f0f4550236827684c78c98eb992ef67a5608a","target":"record","created_at":"2026-05-18T03:13:44Z","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":"415f96b6ee3817acbff1f040b074679abdd9974849dd977b90ee9c0c853479e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2013-09-10T06:11:11Z","title_canon_sha256":"f8d85b8d9c8fa44079c29ee8232937ab984eb0dabafc694fb29135344156e608"},"schema_version":"1.0","source":{"id":"1309.2383","kind":"arxiv","version":1}},"canonical_sha256":"6e6b44064ff1ac2f8d9d1d87300a21605a61f9ecc5d3364c92b015486f0631a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e6b44064ff1ac2f8d9d1d87300a21605a61f9ecc5d3364c92b015486f0631a0","first_computed_at":"2026-05-18T03:13:44.832174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:44.832174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A65ZO850JLoc43AarVjyxzIzdAubzWyzMX6eRpUdRgOz7rWYNP3GtVRlPLS7URijpG0qJeTiEqmxCyfCHlj0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:44.832810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2383","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bde4e6f6d704ce35c95136b225f0f4550236827684c78c98eb992ef67a5608a","sha256:00238e7c1a183ca7ccd62405fd04ce441a57af767c4dbf1035c5d2df48a18719"],"state_sha256":"cc2c4845c42d9068db946091116ff4a3590932b7712ddc37a60cac99ff1d30b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ywsYgmWZO2UQEp7LIi1pSJBZ96u+qZQP9zpTYDzx+Z6FfqCKnKePZj1k1DWyvygSEqd1vy+wO5LMMkUmkexBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T23:58:42.349626Z","bundle_sha256":"00696a7c20ee5037b7a640b5d3adfdca736bc3a6c0add8dcc9c52fca236afb23"}}