{"paper":{"title":"Implied Volatility Expansions for VIX Options in Forward Variance Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Forward variance models admit closed-form expansions for the implied volatility of VIX options.","cross_cats":["q-fin.MF"],"primary_cat":"q-fin.CP","authors_text":"Ankush Agarwal, Florian Bourgey, Ying Liao","submitted_at":"2026-04-28T01:58:10Z","abstract_excerpt":"We develop closed-form expansions for the implied volatility of VIX options within the class of forward variance models. Our approach builds on weak-approximation techniques for VIX option prices and yields explicit implied volatility expansions with computable correction terms. The resulting formulas enable fast and accurate calibration without requiring numerical root-finding using option prices. We illustrate the performance of the proposed expansions in both standard and rough Bergomi-type models, as well as in mixed specifications, and demonstrate their accuracy through numerical experime"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We develop closed-form expansions for the implied volatility of VIX options within the class of forward variance models... yields explicit implied volatility expansions with computable correction terms.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That weak-approximation techniques for VIX option prices remain sufficiently accurate in forward variance models to produce reliable implied volatility expansions with computable corrections across practical parameter ranges.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Closed-form implied volatility expansions for VIX options are derived in forward variance models via weak approximations, with explicit correction terms for fast calibration.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Forward variance models admit closed-form expansions for the implied volatility of VIX options.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1b054ea592245116b80becaf8167d81d4ec795d5de5879a985d0ac650e785649"},"source":{"id":"2604.25123","kind":"arxiv","version":2},"verdict":{"id":"6f8932ac-362a-4c58-903e-b92432edb580","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T13:58:05.579050Z","strongest_claim":"We develop closed-form expansions for the implied volatility of VIX options within the class of forward variance models... yields explicit implied volatility expansions with computable correction terms.","one_line_summary":"Closed-form implied volatility expansions for VIX options are derived in forward variance models via weak approximations, with explicit correction terms for fast calibration.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That weak-approximation techniques for VIX option prices remain sufficiently accurate in forward variance models to produce reliable implied volatility expansions with computable corrections across practical parameter ranges.","pith_extraction_headline":"Forward variance models admit closed-form expansions for the implied volatility of VIX options."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.25123/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T05:38:54.617626Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T21:25:37.528946Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"d18c1c4772da293e52453e4527eeec47376dea3947a4fefa4b945ac731fcc8d8"},"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"}