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Jumps, in particular exponential L\\'evy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see \\cite{Tank} for an overview), and more recently rough volatility models \\cite{AlosLeon, Fukasawa}. We suggest here a different route, randomising the Black-Scholes variance by a CEV-generated distribution, which allows us to modulate the rate of explosion (through the CEV exponent) of the implied vol"},"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":"1503.08082","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2015-03-27T14:05:21Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"1857e4c7347c003f519e0c2ef15faf0ce136c6c894690eff0578558e49ae6f39","abstract_canon_sha256":"59c30ed9b41ca09546d1c936e0695c0a1b36edabe950d4a9df714cbe7b395a6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:33.875211Z","signature_b64":"f3rw2CUG0FX3tir0bU+TEivPC77UuW0oGeuiNaikYBQr6iGwjxADTpLtBzTDXfnYc0GGlEzux30zGG38EdpsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae1c72b657adb8f95b92c3ba92921dc2010c64f7b234e14b3a4c47e026b22b06","last_reissued_at":"2026-05-18T00:29:33.874578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:33.874578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Black-Scholes in a CEV random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.PR","authors_text":"Antoine Jacquier, Patrick Roome","submitted_at":"2015-03-27T14:05:21Z","abstract_excerpt":"Classical (It\\^o diffusions) stochastic volatility models are not able to capture the steepness of small-maturity implied volatility smiles. 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