{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T11:29:52Z","timestamp":1786706992530,"version":"build-2736575974"},"reference-count":62,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T00:00:00Z","timestamp":1786665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The standard models of stock-price dynamics and option valuation rest on stochastic processes postulated at the outset; here, we lay down an entropic-inference framework that derives these processes rather than assuming them, by making explicit the information each one encodes. A symmetry comes first: markets reward returns rather than price levels, which selects the logarithm of price as the dynamical variable. The price then evolves through two channels, a continuous one carrying the constraints of continuity and directionality, and a jump channel carrying the arrival rate and the first two moments of the jump size. Because these constraints act on disjoint parts of the microstate, the channels factorize as a theorem, and the dynamics is the Merton jump-diffusion, with Geometric Brownian Motion as its no-jump limit; the log-price density obeys a Kolmogorov\u2013Feller equation, of which the Fokker\u2013Planck equation is the no-jump limit. The same principle, now imposing no-arbitrage through the mean log-return, selects the Esscher transform from among the many martingale measures an incomplete market admits, here derived rather than borrowed; the premium then satisfies Merton\u2019s partial integro-differential equation, and the risk-neutral mixture of lognormals generates the implied-volatility smile, the Black\u2013Scholes results returning when jumps vanish. What changes from one model to the next is never the inference but the information supplied to it.<\/jats:p>","DOI":"10.3390\/e28080914","type":"journal-article","created":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T10:39:01Z","timestamp":1786703941000},"page":"914","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Entropic Dynamics of Jump-Diffusion Option Pricing"],"prefix":"10.3390","volume":"28","author":[{"given":"Mohammad","family":"Abedi","sequence":"first","affiliation":[{"name":"Van Eck Associates Corporation, New York, NY 10017, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1063\/1.3573619","article-title":"Entropic Inference","volume":"1350","author":"Caticha","year":"2011","journal-title":"AIP Conf. 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