{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T00:50:07Z","timestamp":1791507007224,"version":"4.3.4"},"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":"<div>\n Static no-arbitrage conditions on implied volatility surfaces are usually imposed through a\n<\/div>\n<div>\n parametric form or a training penalty. Parametric fits to sparse, noisy quotes are not auto-\n<\/div>\n<div>\n matically arbitrage-free, and penalties give no confidence away from the points where they are\n<\/div>\n<div>\n applied. As a proof of concept, we ask whether convexity in log-moneyness and monotonicity in\n<\/div>\n<div>\n Maturity can be built into a neural total-variance surface by architecture while it stays trainable.\n<\/div>\n<div>\n with automatic differentiation, and what this costs in accuracy. The network is positive, con-\n<\/div>\n<div>\n vex in log-moneyness and non-decreasing in maturity at every input; it combines input-convex\n<\/div>\n<div>\n blocks gated by non-negative maturity ramps and uses an output-scale calibration at initializa-\n<\/div>\n<div>\n tion. We test it on synthetic data from rejection-sampled arbitrage-free SVI slices with Gaussian\n<\/div>\n<div>\n noise (standard deviation 0.02) and stratified masking, in three regimes with five seeds each,\n<\/div>\n<div>\n against per-slice SVI, SSVI, a soft-penalty MLP, and a Dugas-style ablation, on clean data and\n<\/div>\n<div>\n under a calendar-inversion stress test. On clean data the hard-constrained model has 0.00%.\n<\/div>\n<div>\n convexity, Durrleman, and calendar violations in all 15 runs (tolerance 10\u207b\u2074). The soft penalty\n<\/div>\n<div>\n MLP shows 0.00\u20130.04% convexity, 0.00\u20130.84% Durrleman, and 0.00\u20130.02% calendar violations\n<\/div>\n<div>\n and per-slice SVI shows 2.69\u20133.88% Durrleman and 17.86\u201331.02% calendar violations. The\n<\/div>\n<div>\n guarantee costs accuracy: overall RMSE in total variance is 0.0099, 0.0124, and 0.0176 (normal,\n<\/div>\n<div>\n high-skew, stressed) against 0.0074, 0.0096, and 0.0135 for SSVI and 0.0092, 0.0112, and 0.0154\n<\/div>\n<div>\n for the soft-penalty MLP. Removing the output-scale calibration raises RMSE by about an or<span>der of magnitude. Under a calendar-inversion stress test, the hard-constrained model again has<\/span>\n<\/div>\n<div>\n 0.00% violations, against 0.20% calendar violations for the soft-penalty MLP and 29.86% for\n<\/div>\n<div>\n per-slice SVI, and every model\u2019s accuracy degrades. The data are synthetic and well specified\n<\/div>\n<div>\n for SVI; convexity and monotonicity are guaranteed, whereas Durrleman\u2019s condition is audited\n<\/div>\n<div>\n empirically.\n<\/div><\/jats:p>","DOI":"10.2139\/ssrn.7577418","type":"posted-content","created":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T00:10:21Z","timestamp":1791504621000},"source":"Crossref","is-referenced-by-count":0,"title":["Trainable Hard Constraints: Architectural Enforcement of Arbitrage-Free Implied Volatility Surfaces via Automatic Differentiation"],"prefix":"10.2139","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-4721-0749","authenticated-orcid":true,"given":"Anagha","family":"S","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T00:10:21Z","timestamp":1791504621000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7577418"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7577418","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}