A NOTE ON ESSENTIAL SMOOTHNESS IN THE HESTON MODEL

Abstract. This note studies an issue relating to essential smoothness that can arise when
the theory of large deviations is applied to a certain option pricing formula in the Heston model.
The note identifies a gap, based on this issue, in the proof of Corollary~2.4 in~\cite{FordeJacquier10}
and describes how to circumvent it. This completes the proof of Corollary~2.4 in~\cite{FordeJacquier10}
and hence of the main result in~\cite{FordeJacquier10}, which describes the limiting behaviour of the
implied volatility smile in the Heston model far from maturity.

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