Abstract. We consider the implied volatility of European options in an affine stochastic volatility model with jumps, as time tends to infinity. We show that under a simultaneous rescaling of the option strike a non-degenerate limiting volatility smile exists and describe it by a formula which can be expressed in terms of the parameters of the underlying model. The result is based on a large-deviation principle for affine stochastic volatility models, that is derived via the Gärtner-Ellis theorem. We exhibit some specific examples including a Heston model with and without jumps, Bates' model with state-dependent jump intensity and the Barndorff-Nielsen-Shephard model. This is joint work with Antoine Jacquier and Aleksandar Mijatovic.

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