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Large-Maturity Regimes of the Heston Forward Smile

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  • Antoine Jacquier
  • Patrick Roome

Abstract

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.

Suggested Citation

  • Antoine Jacquier & Patrick Roome, 2014. "Large-Maturity Regimes of the Heston Forward Smile," Papers 1410.7206, arXiv.org, revised Aug 2015.
  • Handle: RePEc:arx:papers:1410.7206
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    12. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082, arXiv.org, revised Nov 2017.
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    Cited by:

    1. Omar El Euch & Mathieu Rosenbaum, 2016. "The characteristic function of rough Heston models," Papers 1609.02108, arXiv.org.
    2. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082, arXiv.org, revised Nov 2017.
    3. repec:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0197-5 is not listed on IDEAS

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