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Large-maturity regimes of the Heston forward smile

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  • Jacquier, Antoine
  • Roome, Patrick

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

  • Jacquier, Antoine & Roome, Patrick, 2016. "Large-maturity regimes of the Heston forward smile," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1087-1123.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:4:p:1087-1123
    DOI: 10.1016/j.spa.2015.10.012
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    Cited by:

    1. Elisa Alos & Antoine Jacquier & Jorge Leon, 2017. "The implied volatility of Forward-Start options: ATM short-time level, skew and curvature," Papers 1710.11232, arXiv.org.
    2. Omar El Euch & Mathieu Rosenbaum, 2016. "The characteristic function of rough Heston models," Papers 1609.02108, arXiv.org.
    3. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082, arXiv.org, revised Nov 2017.
    4. Oliver Pfante & Nils Bertschinger, 2016. "Uncertainty Estimates in the Heston Model via Fisher Information," Papers 1610.04760, arXiv.org, revised Oct 2016.
    5. M. Papi & L. Pontecorvi & C. Donatucci, 2017. "Weighted average price in the Heston stochastic volatility model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 351-373, November.

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