{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T12:40:17Z","timestamp":1792845617944,"version":"4.5.0"},"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:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Zero-days-to-expiration (0DTE) options on the S&amp;amp;P 500 now account for roughly half of SPX option volume, yet their risk is still summarised with Black-Scholes partial derivatives that treat spot, implied volatility and time as independent. Using five-minute quotes for the full SPXW 0DTE chain on 1,108 trading days (May 2022-October 2026), I document that over the 6.5-hour life of these contracts the three state variables move together in a predictable, time-of-day-dependent and asymmetric way: at-the-money implied volatility responds to a 1% index fall by 6.7 volatility points but to a 1% rise by only 4.1, with the asymmetry tripling in the final half hour; the intraday skew-stickiness ratio is 2.2-2.8, above the short-maturity diffusive bound of 2; and realised time decay of the at-the-money straddle is twice the Black-Scholes theta in the first hour and two thirds of it in the last. I define Upsilon (\u03a5), a single effective sensitivity equal to the expected option value change along the empirically estimated joint intraday dynamics, with a directional pair (\u03a5\u207a, \u03a5\u207b) and a business-clock temporal component. Empirically, the same Greek displays two regimes within one contract: before 13:30 ET, \u03a5\u207a and \u03a5\u207b are statistically indistinguishable but both sit 20-25% below the Black-Scholes delta for calls while the temporal component runs at twice the Black-Scholes theta; after 13:30 they diverge sharply, reaching 40-45% of the delta in the last half hour for both puts and calls, always in the direction adverse to the option holder. As a hedge ratio, \u03a5 reduces the out-of-sample mean absolute hedging error by 4.3-5.7% relative to Black-Scholes delta (day-clustered t \u2248-20), every year from 2022 to 2026, whereas the Hull-White minimum-variance delta yields no improvement; the gain is concentrated in calls and far-out-of-the-money contracts, because for 0DTE puts the Black-Scholes delta is already within 5% of the minimum-variance hedge. No method reduces squared hedging error, because 57-66% of it is generated by the largest 1% of five-minute moves-the jump component that short-maturity theory predicts to be undiversifiable by delta hedging. The results reposition 0DTE risk management from \"which delta\" to \"which direction and which hour\".<\/jats:p>","DOI":"10.2139\/ssrn.7663319","type":"posted-content","created":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T12:03:16Z","timestamp":1792843396000},"source":"Crossref","is-referenced-by-count":0,"title":["Upsilon: A Joint Spot-Volatility-Time Sensitivity for Zero-Days-to-Expiration Index Options"],"prefix":"10.2139","author":[{"given":"Jonathan","family":"Klip","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T12:03:16Z","timestamp":1792843396000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7663319"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7663319","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}