{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T19:59:03Z","timestamp":1790711943148,"version":"4.1.0"},"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>A digital option has a Gamma that changes sign at the strike, which makes it the textbook case in which the uncertain volatility model (UVM) of Avellaneda, Levy and Par\u00e1s differs from Black-Scholes evaluated at the ends of the volatility band. I price a one-year cash-or-nothing call with volatility known only to lie in [15%, 25%] and study how far static positions in traded calls narrow the resulting bid-ask interval. The model is solved with a fully implicit, monotone finite-difference scheme with policy iteration, validated against closed-form Black-Scholes prices. Three results matter in practice. First, because the UVM is non-linear, a hedged position must be priced as a single portfolio: pricing the legs separately and summing, as is often done, produces a spread of 0.575 against a correct 0.136, and makes hedging appear to widen rather than narrow the interval. Second, optimising the hedge notionals (a convex problem) cuts the unhedged spread of 0.243 by 51% with a 90\/110 call spread, 69% with a 95\/105 spread and 78% with five strikes. Third, the benefit is fragile to transaction costs: a bid-ask of \u00b11 volatility point around mid on the vanillas leaves only a 20% reduction. A hedge instrument that expires before the digital still delivers most of the benefit once handled through the correct jump condition.<\/jats:p>","DOI":"10.2139\/ssrn.7539043","type":"posted-content","created":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T19:00:41Z","timestamp":1790708441000},"source":"Crossref","is-referenced-by-count":0,"title":["Pricing and Statically Hedging a Digital Option under Uncertain Volatility A corrected and extended treatment"],"prefix":"10.2139","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-9306-5248","authenticated-orcid":true,"given":"Luigi","family":"Piva","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T19:00:41Z","timestamp":1790708441000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7539043"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7539043","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}