{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T08:45:12Z","timestamp":1792140312687,"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:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>A short option position hedged with the underlying asset carries, between rebalancing dates, a hedge error: the difference between the model delta and the share holding. Correcting it incurs a fixed cost per trade and a cost proportional to the traded value. We determine the cost-optimal size of the correction in a one-period model. To leading order in the horizon, the P&amp;amp;L attributable to the hedge error is linear in the error; any nonlinearity in the value of a correction therefore originates in the risk functional used to evaluate that P&amp;amp;L. We prove a general criterion: for a convex risk functional \u03c1, an interior (partial) correction is optimal only if the proportional cost per unit traded lies in the interval (\u03c1 (0 +), \u03c1 (u)), where u is the current hedge error. A risk functional linear in the P&amp;amp;L standard deviation gives an empty interval and hence only full or zero corrections; a functional quadratic in it gives an interval with lower endpoint zero. For a functional containing both terms, the optimal correction is obtained in closed form. The parameter space divides into three regions (full, partial, none) whose boundaries are given explicitly and meet at a triple point. The relative width of the partial region equals \u03b3uS\u03c3 \u221a h\/\u03bb, the ratio of the quadratic to the linear coefficient scaled by the error. We also analyse an earlier exponential risk functional that produced a partial optimum only for proportional costs near 24%, and identify the error in it. A Monte Carlo simulation of the 20-week call example of Hull compares the rule with full rebalancing on a fixed schedule.<\/jats:p>","DOI":"10.2139\/ssrn.7613519","type":"posted-content","created":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T08:06:28Z","timestamp":1792137988000},"source":"Crossref","is-referenced-by-count":0,"title":["Partial Rebalancing of a Delta Hedge Under Fixed and Proportional Transaction Costs: A Three-Phase Solution"],"prefix":"10.2139","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7651-1817","authenticated-orcid":true,"given":"Gagandeep","family":"Singh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T08:06:28Z","timestamp":1792137988000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7613519"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7613519","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}