Large deviations for the extended Heston model: the large-time case - Jacquier,A; Mijatovic,A (Asia-Pacific Financial Markets, 2014)
We study here the large-time behaviour of all continuous affine stochasticvolatility models (in the sense of Keller-Ressel) and deduce a closed-formformula for the large-maturity implied volatility smile. Based on refinementsof the Gartner-Ellis theorem on the real line, our proof reveals pathologicalbehaviours of the asymptotic smile. In particular, we show that the conditionassumed in Gatheral and Jacquier under which the Heston implied volatilityconverges to the SVI parameterisation is necessary and sufficient.