{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EZZUJYNHPJPIZWQ7Y4HZ3DAYBI","short_pith_number":"pith:EZZUJYNH","canonical_record":{"source":{"id":"1409.5801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2014-09-19T20:01:09Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"72cb1cf96c385426431f4f465abb36a5c6a253b14fcc6e14bb75891b6fd5ff53","abstract_canon_sha256":"cd8325e8a6d24aace60d22060f629a311eca93b21807bfc133ff9c4b98478965"},"schema_version":"1.0"},"canonical_sha256":"267344e1a77a5e8cda1fc70f9d8c180a1ef72835a0be5fdfc224d54785bf90bc","source":{"kind":"arxiv","id":"1409.5801","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5801","created_at":"2026-05-18T02:42:16Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5801v1","created_at":"2026-05-18T02:42:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5801","created_at":"2026-05-18T02:42:16Z"},{"alias_kind":"pith_short_12","alias_value":"EZZUJYNHPJPI","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EZZUJYNHPJPIZWQ7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EZZUJYNH","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EZZUJYNHPJPIZWQ7Y4HZ3DAYBI","target":"record","payload":{"canonical_record":{"source":{"id":"1409.5801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2014-09-19T20:01:09Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"72cb1cf96c385426431f4f465abb36a5c6a253b14fcc6e14bb75891b6fd5ff53","abstract_canon_sha256":"cd8325e8a6d24aace60d22060f629a311eca93b21807bfc133ff9c4b98478965"},"schema_version":"1.0"},"canonical_sha256":"267344e1a77a5e8cda1fc70f9d8c180a1ef72835a0be5fdfc224d54785bf90bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:16.053147Z","signature_b64":"L1CBMms9/Xy7FwrOQbIr0nwjzJZkRW99ytBmWbd+YFuKKdyjbZTDRMgAjzLU1cbUVCiC2JWVk0IYyMkdEIhsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"267344e1a77a5e8cda1fc70f9d8c180a1ef72835a0be5fdfc224d54785bf90bc","last_reissued_at":"2026-05-18T02:42:16.052484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:16.052484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.5801","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":"2026-05-18T02:42:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BaHb9DcY28XMrbaKGnjXSUzGs7oeGsPGimoi7W+2hGEO9qZ1sqp4EWUjLA3w9vrbIbUtAXhHkGpkuhJTu9pECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T04:31:57.703897Z"},"content_sha256":"2fcf0f73a144934373250e33a08913f1547f51bcc78060634086b5187c3da4ea","schema_version":"1.0","event_id":"sha256:2fcf0f73a144934373250e33a08913f1547f51bcc78060634086b5187c3da4ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EZZUJYNHPJPIZWQ7Y4HZ3DAYBI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pricing and hedging of energy spread options and volatility modulated Volterra processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.PR","authors_text":"Fred Espen Benth, Hanna Zdanowicz","submitted_at":"2014-09-19T20:01:09Z","abstract_excerpt":"We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of power and gas. Volatility modulated Volterra processes are in general not semimartingales, but contain several special cases of interest in energy markets like for example continuous-time autoregressive moving average processes. Based on a change of measure, we obtain a pricing expression based on a univariate Fourier transform of the payoff function and the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5801","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":"2026-05-18T02:42:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZT0rRNMTfzdMLiPvqu0yd3pkSmvDI0N7zHCfYO5tvooE/+fBnZgEcay+8xQm+E0Rt9A+lWz5RfxLcPzgdfaCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T04:31:57.704602Z"},"content_sha256":"34e256b4bd3bf26bec3fb9533f7b74214ab9cae9cc97438d1737d80b972955b9","schema_version":"1.0","event_id":"sha256:34e256b4bd3bf26bec3fb9533f7b74214ab9cae9cc97438d1737d80b972955b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EZZUJYNHPJPIZWQ7Y4HZ3DAYBI/bundle.json","state_url":"https://pith.science/pith/EZZUJYNHPJPIZWQ7Y4HZ3DAYBI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EZZUJYNHPJPIZWQ7Y4HZ3DAYBI/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":"2026-05-23T04:31:57Z","links":{"resolver":"https://pith.science/pith/EZZUJYNHPJPIZWQ7Y4HZ3DAYBI","bundle":"https://pith.science/pith/EZZUJYNHPJPIZWQ7Y4HZ3DAYBI/bundle.json","state":"https://pith.science/pith/EZZUJYNHPJPIZWQ7Y4HZ3DAYBI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EZZUJYNHPJPIZWQ7Y4HZ3DAYBI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EZZUJYNHPJPIZWQ7Y4HZ3DAYBI","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":"cd8325e8a6d24aace60d22060f629a311eca93b21807bfc133ff9c4b98478965","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2014-09-19T20:01:09Z","title_canon_sha256":"72cb1cf96c385426431f4f465abb36a5c6a253b14fcc6e14bb75891b6fd5ff53"},"schema_version":"1.0","source":{"id":"1409.5801","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5801","created_at":"2026-05-18T02:42:16Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5801v1","created_at":"2026-05-18T02:42:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5801","created_at":"2026-05-18T02:42:16Z"},{"alias_kind":"pith_short_12","alias_value":"EZZUJYNHPJPI","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EZZUJYNHPJPIZWQ7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EZZUJYNH","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:34e256b4bd3bf26bec3fb9533f7b74214ab9cae9cc97438d1737d80b972955b9","target":"graph","created_at":"2026-05-18T02:42:16Z","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 the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of power and gas. Volatility modulated Volterra processes are in general not semimartingales, but contain several special cases of interest in energy markets like for example continuous-time autoregressive moving average processes. Based on a change of measure, we obtain a pricing expression based on a univariate Fourier transform of the payoff function and the c","authors_text":"Fred Espen Benth, Hanna Zdanowicz","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2014-09-19T20:01:09Z","title":"Pricing and hedging of energy spread options and volatility modulated Volterra processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5801","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":"sha256:2fcf0f73a144934373250e33a08913f1547f51bcc78060634086b5187c3da4ea","target":"record","created_at":"2026-05-18T02:42:16Z","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":"cd8325e8a6d24aace60d22060f629a311eca93b21807bfc133ff9c4b98478965","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2014-09-19T20:01:09Z","title_canon_sha256":"72cb1cf96c385426431f4f465abb36a5c6a253b14fcc6e14bb75891b6fd5ff53"},"schema_version":"1.0","source":{"id":"1409.5801","kind":"arxiv","version":1}},"canonical_sha256":"267344e1a77a5e8cda1fc70f9d8c180a1ef72835a0be5fdfc224d54785bf90bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"267344e1a77a5e8cda1fc70f9d8c180a1ef72835a0be5fdfc224d54785bf90bc","first_computed_at":"2026-05-18T02:42:16.052484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:16.052484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L1CBMms9/Xy7FwrOQbIr0nwjzJZkRW99ytBmWbd+YFuKKdyjbZTDRMgAjzLU1cbUVCiC2JWVk0IYyMkdEIhsCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:16.053147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5801","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fcf0f73a144934373250e33a08913f1547f51bcc78060634086b5187c3da4ea","sha256:34e256b4bd3bf26bec3fb9533f7b74214ab9cae9cc97438d1737d80b972955b9"],"state_sha256":"e6b36878eb381eebff069ac589c4210d9e6183efe077fa27193c52e8ab6b9ca2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B8ar1O6l5Y3XJYk7xxA5Q46E98Ug5KDivZFgrMOlIxy8I1XOMUiJy+Aev1QcY42QTaObIabS+ETKQVciOhDSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T04:31:57.708818Z","bundle_sha256":"734ccbdfed13b2d357c527439ca6793669aabb55f922cb3e5dcf1f9c9ad22e26"}}