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

Abstract

We study here the large-time behavior of all continuous affine stochastic volatility models (in the sense of Keller-Ressel) and deduce a closed-form formula for the large-maturity implied volatility smile. Based on refinements of the Gartner-Ellis theorem on the real line, our proof reveals pathological behaviors of the asymptotic smile. In particular, we show that the condition assumed in Gatheral & Jacquier (GJ10) under which the Heston implied volatility converges to the SVI parameterization is necessary and sufficient.

Keywords: Heston, large maturity, asymptotics, large deviations

JEL Classification: G12, G13, C60, C63