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Asymptotics of forward implied volatility


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  • Antoine Jacquier
  • Patrick Roome
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    We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility smile in a large class of models, including Heston and time-changed exponential Levy models. This expansion applies to both small and large maturities and is based solely on the knowledge of the forward characteristic function of the underlying process.The method is based on sharp large deviations techniques, and allows us to recover (in particular) many results for the spot implied volatility smile. In passing we show (i) that the small-maturity exploding behaviour of forward smiles depends on whether the quadratic variation of the underlying is bounded or not, and (ii) that the forward-start date also has to be rescaled in order to obtain non-trivial small-maturity asymptotics.

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    Bibliographic Info

    Paper provided by in its series Papers with number 1212.0779.

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    Date of creation: Dec 2012
    Date of revision: Oct 2013
    Handle: RePEc:arx:papers:1212.0779

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