We study here the large-time behaviour of all continuous affine stochastic volatility models [in the sense of Keller-Ressel (Math Finan 21(1):73–98, <CitationRef CitationID="CR14">2011</CitationRef>)] and deduce a closed-form formula for the large-maturity implied volatility smile. We concentrate on (rescaled) strikes around the money,...</citationref>

The purpose of this paper is to improve and discuss the asymptotic formula of the implied volatility (when maturity goes to infinity) given in [3]. Indeed, we are here able to provide more accurate at-the-money asymptotics. Such analytic formulas are useful for calibration.