Large Deviations for the Extended Heston Model: The Large-Time Case

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, which are the most common in practice, and extend the results in Forde and Jacquier (Finan Stoch 15(4):755–780, <CitationRef CitationID="CR4">2011</CitationRef>) and Gatheral and Jacquier (Quant Finan 11(8):1129–1132, <CitationRef CitationID="CR8">2011</CitationRef>). Copyright Springer Japan 2014