{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T01:55:03Z","timestamp":1787363703595,"version":"build-2736575974"},"reference-count":58,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox--Ingersoll--Ross model, is multiplied by a (leverage) function of the spot process, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for the spot process with the full truncation Euler scheme or the backward Euler--Maruyama scheme for the squared stochastic volatility component. Under some mild regularity assumptions and a condition on the Feller ratio, we establish the strong convergence with order 1\/2 (up to a logarithmic factor) of the approximation process up to a critical time. The model studied in this paper contains as special cases Heston-type stochastic-local volatility models, the state of the art in derivative pricing, and a relatively new class of path-dependent volatility models. The present paper is the first to prove the convergence of the popular Euler schemes with a positive rate, which is moreover consistent with that for Lipschitz coefficients and hence optimal.<\/jats:p>","DOI":"10.1137\/17m1136754","type":"journal-article","created":{"date-parts":[[2018,12,11]],"date-time":"2018-12-11T14:09:26Z","timestamp":1544537366000},"page":"3430-3458","source":"Crossref","is-referenced-by-count":1,"title":["Strong Convergence Rates for Euler Approximations to a Class of Stochastic Path-Dependent Volatility Models"],"prefix":"10.1137","volume":"56","author":[{"given":"Andrei","family":"Cozma","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christoph","family":"Reisinger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,12,11]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1515\/156939605777438569"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2012.10.034"},{"key":"atypb3","first-page":"1930","volume":"37","author":"Altmayer M.","year":"2017","journal-title":"IMA J. 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