{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T23:49:27Z","timestamp":1791416967046,"version":"4.3.3"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":32,"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-expiry (0DTE) options reached 51% of S&amp;amp;P 500 index (SPX) options volume in Q4 2024 and 59% of full-year 2025 volume (Cboe), making short-dated Greeks central to intraday gamma-exposure analytics. We identify a systematic, state-dependent bias in those Greeks that arises from a common design in hybrid volatility engines. A smoothed volatility surface is calibrated only from expiries at or beyond a minimum grid maturity-about two weeks in the system studied-so contracts below that floor have no surface node and a na\u00efve Greeks path evaluates them at the floor node's volatility. This cross-maturity volatility substitution is silentevery surface diagnostic stays clean-and directionally structured under short-end inversion, with near-the-money gamma systematically overstated: gamma scales as 1\/(\u03c3\u221aT), so a floor volatility below the true short-dated level inflates near-ATM gamma in proportion. Across 49 real SPX sessions (41 with open interest), an engine-free reconstruction that substitutes the observable implied floor misestimates 0-2-day-to-expiry gamma by a median 47%. Its all-sub-floor gamma error is 9.1% under open-interest weighting and 14.5% under equal weighting; the corresponding 0-7-day-bucket errors are 16.6% and 22.1%. A median 25% of gross dollar-gamma exposure sits below the floor, while the signed whole-book aggregate nearly cancels-the aggregate-level invisibility that let the defect persist. Every error measure rises with short-end term-structure inversion (Spearman \u03c1 = +0.53 for the substituted volatility and +0.39-0.50 for the induced gamma errors, all p &amp;lt; 0.05)-the bias hides on calm days and bites on stressed ones. The fix is minimal-evaluate sub-floor Greeks at each contract's own-maturity calibrated volatility. In the archived production engine, whose grid stores a local-volatility floor, it shifts gross aggregate gamma by +3.6% and absolute theta by-9.7%, with open-interest metrics unchanged. It also moves the published strike-profile GEX crossing-the level commonly reported as the \"gamma flip\"-by 24 index points, while the canonical portfolio zero-gamma root, obtained by repricing the book across spot, moves only 1.9: the reported level is markedly more sensitive to the defect than the regime boundary it is taken to represent. The reconstruction is engine-free and fully specified hereindata filters, metric definitions, and constants-so it can be repeated on any equivalent vendor chain dataset. This is a measurement and reproducibility contribution, not a trading signal; it is a companion to our treatment of the dealer-gamma sign convention (Chilingarian 2026).<\/jats:p>","DOI":"10.2139\/ssrn.7205361","type":"posted-content","created":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T10:32:12Z","timestamp":1786098732000},"source":"Crossref","is-referenced-by-count":0,"title":["Three Clocks, One Option: Cross-Maturity Volatility Substitution and the State-Dependent Short-Dated Greeks Bias in Real-Time S&amp;amp;P 500 Analytics"],"prefix":"10.2139","author":[{"given":"Aren","family":"Chilingarian","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"ref1","journal-title":"Take one chain snapshot at 10:00 ET (America\/New_York) carrying, per contract, strike, expiry, calendar DTE, root, option type, bid, ask, open interest attributed per root, and an implied volatility, plus the underlying level"},{"key":"ref2","journal-title":"Apply the filters of Section 6.1 (volatility in"},{"key":"ref3","journal-title":"-settled standard SPX on its own expiry morning excluded)"},{"key":"ref4","journal-title":"For floor parameter F, set the floor expiry to the first listed expiry with calendar DTE \u2265 F + 1 (equivalently \u03c4 route > F at a 10:00 ET snapshot). The sub-floor set B is every contract expiring before it"},{"key":"ref5","journal-title":"Build the floor smile: call\/put-averaged implied volatility of the floor expiry by strike, interpolated linearly in log-moneyness and flat beyond its quoted range; evaluate it at each sub-floor contract's log-moneyness to obtain \u03c3 flr"},{"key":"ref6","first-page":"10","journal-title":"Compute exact gammas by equation (1) under \u03c3 own and \u03c3 flr at T i = max((DTE calendar,i + f t )\/365"},{"key":"ref7","journal-title":"Form the metrics of Section 5.1 under open-interest and equal weights, the DTE-band and moneyness-band cells, the signed at-the-money and wing ratios, and the signed per-band mean of \u03c3 flr -\u03c3 own for 0-2-day contracts"},{"key":"ref8","journal-title":"Compute the strike-profile crossings and the portfolio zero-gamma root under both volatility assignments as in the companion paper's Appendix C (Model A, \u00b110% window, 201-point grid, bisection), on the book with DTE \u2265 1 and on the whole book"},{"key":"ref9","journal-title":"Record the within-chain slopes (six-nearest-strike at-the-money levels; 1-day, 2-day, floor and 30day legs) and a state variable external to the metric"},{"key":"ref10","year":"2025","journal-title":"Across sessions, take quantiles, bucket tables and Spearman correlations with moving-block bootstrap intervals; repeat steps 3-7 for each F. Expected values on the reference session"},{"key":"ref11","journal-title":"\u0394\u0393 book = +0.65%, slope 0.0657; book with DTE \u2265 1: crossings 7"},{"issue":"3","key":"ref12","first-page":"1335","article-title":"Inputs are licensed vendor and exchange data and are not redistributed; equivalent products differ in quote References","volume":"72","author":"T G Andersen","year":"2017","journal-title":"Journal of Finance"},{"issue":"1","key":"ref13","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.jfineco.2021.04.029","article-title":"Hedging demand and market intraday momentum","volume":"142","author":"G Baltussen","year":"2021","journal-title":"Journal of Financial Economics"},{"issue":"5","key":"ref14","doi-asserted-by":"crossref","first-page":"2003","DOI":"10.1111\/j.1540-6261.1997.tb02749.x","article-title":"Empirical performance of alternative option pricing models","volume":"52","author":"G Bakshi","year":"1997","journal-title":"Journal of Finance"},{"key":"ref15","author":"F M Bandi","year":"2023"},{"key":"ref16","article-title":"Retail traders love 0DTE options\u2026 but should they? Working paper","volume":"4404704","author":"H Beckmeyer","year":"2023","journal-title":"SSRN"},{"issue":"6","key":"ref17","doi-asserted-by":"crossref","first-page":"2581","DOI":"10.1046\/j.1540-6261.2003.00616.x","article-title":"What type of process underlies options? A simple robust test","volume":"58","author":"P Carr","year":"2003","journal-title":"Journal of Finance"},{"issue":"3","key":"ref18","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1093\/rfs\/hhn038","article-title":"Variance risk premiums","volume":"22","author":"P Carr","year":"2009","journal-title":"Review of Financial Studies"},{"key":"ref19","year":"2025","journal-title":"Cboe Global Markets reports trading volume for December and full year 2024"},{"key":"ref20","year":"2026","journal-title":"Cboe Global Markets reports trading volume for December and full year 2025"},{"key":"ref21","author":"A Chilingarian","year":"2026","journal-title":"The sign of dealer gamma: an inventory convention, a scale, and two definitions of the gamma flip in S&P 500 gamma exposure"},{"key":"ref22","author":"C Dim","year":"2024","journal-title":"0DTEs: Trading, gamma risk and volatility propagation. Working paper"},{"issue":"1","key":"ref23","first-page":"18","article-title":"Pricing with a smile","volume":"7","author":"B Dupire","year":"1994","journal-title":"Risk"},{"key":"ref24","author":"J Gatheral","year":"2006","journal-title":"The Volatility Surface: A Practitioner's Guide"},{"issue":"1","key":"ref25","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1080\/14697688.2013.819986","article-title":"Arbitrage-free SVI volatility surfaces","volume":"14","author":"J Gatheral","year":"2014","journal-title":"Quantitative Finance"},{"issue":"3","key":"ref26","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1016\/j.jfineco.2012.06.010","article-title":"Pinning in the S&P 500 futures","volume":"106","author":"B Golez","year":"2012","journal-title":"Journal of Financial Economics"},{"key":"ref27","first-page":"84","article-title":"Managing smile risk","author":"P S Hagan","year":"2002","journal-title":"Wilmott Magazine"},{"key":"ref28","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.jbankfin.2017.05.006","article-title":"Optimal delta hedging for options","volume":"82","author":"J Hull","year":"2017","journal-title":"Journal of Banking & Finance"},{"key":"ref29","volume":"10","author":"J C Hull","year":"2018","journal-title":"Options, Futures, and Other Derivatives"},{"issue":"3","key":"ref30","doi-asserted-by":"crossref","first-page":"2339","DOI":"10.1111\/jofi.13337","article-title":"Nonstandard errors","volume":"79","author":"A J Menkveld","year":"2024","journal-title":"Journal of Finance"},{"issue":"1","key":"ref31","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.jfineco.2004.08.005","article-title":"Stock price clustering on option expiration dates","volume":"78","author":"S X Ni","year":"2005","journal-title":"Journal of Financial Economics"},{"issue":"4","key":"ref32","doi-asserted-by":"crossref","first-page":"1952","DOI":"10.1093\/rfs\/hhaa082","article-title":"Does option trading have a pervasive impact on underlying stock prices?","volume":"34","author":"S X Ni","year":"2021","journal-title":"Review of Financial Studies"}],"container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T22:55:04Z","timestamp":1791413704000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7205361"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":32,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7205361","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}