{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:3L7LV5CIA5WI3SDZLVK7GTYQ7P","short_pith_number":"pith:3L7LV5CI","schema_version":"1.0","canonical_sha256":"dafebaf448076c8dc8795d55f34f10fbf7fd466f01ac66388be44d38bee83620","source":{"kind":"arxiv","id":"1006.2294","version":2},"attestation_state":"computed","paper":{"title":"Small-Time Asymptotics of Option Prices and First Absolute Moments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.PR","authors_text":"Johannes Muhle-Karbe, Marcel Nutz","submitted_at":"2010-06-11T13:21:51Z","abstract_excerpt":"We study the leading term in the small-time asymptotics of at-the-money call option prices when the stock price process $S$ follows a general martingale. This is equivalent to studying the first centered absolute moment of $S$. We show that if $S$ has a continuous part, the leading term is of order $\\sqrt{T}$ in time $T$ and depends only on the initial value of the volatility. Furthermore, the term is linear in $T$ if and only if $S$ is of finite variation. The leading terms for pure-jump processes with infinite variation are between these two cases; we obtain their exact form for stable-like "},"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":"1006.2294","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2010-06-11T13:21:51Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"35c4051a96137dc7e0b0e9445587f449eec0b3bad1749615a5df4aea058489b1","abstract_canon_sha256":"a3a2e42e2bb9afaada8b119e27eb2d7ce08d9525093e43fb173fe6bee7e7c6fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:13.880530Z","signature_b64":"o6qjUP+K35++7xNwqYKasb2ft4rqUHya9vjUD+RZR+L+iUJ5Vvem6UmZnfsW8hpLNEpmR5sm96Mno2siW95xAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dafebaf448076c8dc8795d55f34f10fbf7fd466f01ac66388be44d38bee83620","last_reissued_at":"2026-05-17T23:41:13.880059Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:13.880059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Small-Time Asymptotics of Option Prices and First Absolute Moments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.PR","authors_text":"Johannes Muhle-Karbe, Marcel Nutz","submitted_at":"2010-06-11T13:21:51Z","abstract_excerpt":"We study the leading term in the small-time asymptotics of at-the-money call option prices when the stock price process $S$ follows a general martingale. This is equivalent to studying the first centered absolute moment of $S$. We show that if $S$ has a continuous part, the leading term is of order $\\sqrt{T}$ in time $T$ and depends only on the initial value of the volatility. Furthermore, the term is linear in $T$ if and only if $S$ is of finite variation. The leading terms for pure-jump processes with infinite variation are between these two cases; we obtain their exact form for stable-like "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2294","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1006.2294","created_at":"2026-05-17T23:41:13.880124+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.2294v2","created_at":"2026-05-17T23:41:13.880124+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2294","created_at":"2026-05-17T23:41:13.880124+00:00"},{"alias_kind":"pith_short_12","alias_value":"3L7LV5CIA5WI","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"3L7LV5CIA5WI3SDZ","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"3L7LV5CI","created_at":"2026-05-18T12:26:03.138858+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/3L7LV5CIA5WI3SDZLVK7GTYQ7P","json":"https://pith.science/pith/3L7LV5CIA5WI3SDZLVK7GTYQ7P.json","graph_json":"https://pith.science/api/pith-number/3L7LV5CIA5WI3SDZLVK7GTYQ7P/graph.json","events_json":"https://pith.science/api/pith-number/3L7LV5CIA5WI3SDZLVK7GTYQ7P/events.json","paper":"https://pith.science/paper/3L7LV5CI"},"agent_actions":{"view_html":"https://pith.science/pith/3L7LV5CIA5WI3SDZLVK7GTYQ7P","download_json":"https://pith.science/pith/3L7LV5CIA5WI3SDZLVK7GTYQ7P.json","view_paper":"https://pith.science/paper/3L7LV5CI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.2294&json=true","fetch_graph":"https://pith.science/api/pith-number/3L7LV5CIA5WI3SDZLVK7GTYQ7P/graph.json","fetch_events":"https://pith.science/api/pith-number/3L7LV5CIA5WI3SDZLVK7GTYQ7P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3L7LV5CIA5WI3SDZLVK7GTYQ7P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3L7LV5CIA5WI3SDZLVK7GTYQ7P/action/storage_attestation","attest_author":"https://pith.science/pith/3L7LV5CIA5WI3SDZLVK7GTYQ7P/action/author_attestation","sign_citation":"https://pith.science/pith/3L7LV5CIA5WI3SDZLVK7GTYQ7P/action/citation_signature","submit_replication":"https://pith.science/pith/3L7LV5CIA5WI3SDZLVK7GTYQ7P/action/replication_record"}},"created_at":"2026-05-17T23:41:13.880124+00:00","updated_at":"2026-05-17T23:41:13.880124+00:00"}