Cao, JilingGong, ShengLi, XiZhang, Wenjun2026-05-132026-05-132026-05-13Mathematics, ISSN: 2227-7390 (Online), MDPI AG, 14(10), 1651-1651. doi: 10.3390/math141016512227-7390http://hdl.handle.net/10292/21066<jats:p>In this paper, the valuation of barrier options is studied when the underlying asset is driven by a hybrid model of stochastic volatility and constant elasticity of variance. Using an asymptotic expansion approach and the Fourier transform method, a semi-analytical approximate pricing formula for up-and-out call options are derived under the proposed hybrid model. We validate the approximate pricing formula by comparing its outputs with those produced by Monte Carlo simulation and the binomial tree method. In addition, we perform a sensitivity analysis numerically on the key model parameters and investigate limiting regimes of the hybrid model. It is verified that the approximation is properly anchored to simpler benchmark models when one or both perturbative effects vanish.</jats:p>Copyright: © 2026 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.https://creativecommons.org/licenses/by/4.0/49 Mathematical sciencesasymptoticbarrier optionelasticity of variancestochastic volatilityup-and-out callFourier transformJournal ArticleOpenAccess10.3390/math14101651