Large-Maturity Regimes of the Heston Forward Smile
Stochastic Processes and Their Applications, 126: 1087-1123, 2016
30 Pages Posted: 29 Oct 2014 Last revised: 28 Mar 2016
Date Written: October 27, 2014
We provide a full characterisation of the large-maturity forward implied volatility smile in the Heston model. Although the leading decay is provided by a fairly classical large deviations behaviour, the algebraic expansion providing the higher-order terms highly depends on the parameters, and different powers of the maturity come into play. As a by-product of the analysis we provide new implied volatility asymptotics, both in the forward case and in the spot case, as well as extended SVI-type formulae. The proofs are based on extensions and refinements of sharp large deviations theory, in particular in cases where standard convexity arguments fail.
Keywords: Stochastic volatility, Heston, forward implied volatility, asymptotic expansion, sharp large deviations.
JEL Classification: 60F10, 91G99, 91G60
Suggested Citation: Suggested Citation