{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T16:47:07Z","timestamp":1792082827481,"version":"4.4.0"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":0,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.uspto.gov\/ip-policy\/copyright-policy\/copyright-basics"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Recent empirical work finds that asset return volatility is rough, with a Hurst index H well below 1\/2, placing it outside the semimartingale framework that underlies high-frequency econometrics. We develop an It\u00f4-type calculus adapted to this roughness and use it to draw inference on two quantities of central economic interest: the leverage effect and the roughness index H itself. The construction proceeds by lifting the spot volatility to a two-parameter process on which ordinary stochastic calculus applies, then pulling the expansion back to the spot process. This yields a rough It\u00f4 formula and a principal-residual decomposition that separates the informative part of a high-frequency statistic from a bias of explicit order. Building on this foundation, we extend leverage effect estimation to the rough volatility setting and derive bias-corrected nonparametric estimators with feasible central limit theorems (CLT). The dependence of these estimators on the time lag carries information about H, and we exploit this to develop a rate-optimal estimator of roughness with a feasible CLT, valid also in the semimartingale case. In an empirical application to S&amp;amp;P 500 intra-day transaction data over 2018-2025, the leverage-based estimates of H fall below 1\/2 throughout most of the sample, and the semimartingale hypothesis is rejected for the majority of the period since mid-2020.<\/jats:p>","DOI":"10.2139\/ssrn.7615661","type":"posted-content","created":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T15:51:12Z","timestamp":1792079472000},"source":"Crossref","is-referenced-by-count":0,"title":["An It\u00f4-type Formula: High Frequency Estimation under Rough Volatility"],"prefix":"10.2139","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-8521-3632","authenticated-orcid":true,"given":"Haijian","family":"GUO","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dachuan","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenxu","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Per A.","family":"Mykland","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T15:51:12Z","timestamp":1792079472000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7615661"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7615661","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}