A note on essential smoothness in the Heston model

2011/07/25 by Martin Forde, Forde, Martin, Antoine Jacquier +3
Economics, Econometrics and Finance · #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1107.4881

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 \citeFordeJacquier10 and describes how to circumvent it. This completes the proof of Corollary 2.4 in \citeFordeJacquier10 and hence of the main result in \citeFordeJacquier10, which describes the limiting behaviour of the implied volatility smile in the Heston model far from maturity.

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