The Small-maturity Heston Forward Smile Antoine Jacquier and Patrick Roome

نویسندگان

  • ANTOINE JACQUIER
  • PATRICK ROOME
چکیده

In this paper we investigate the asymptotics of forward-start options and the forward implied volatility smile in the Heston model as the maturity approaches zero. We prove that the forward smile for out-ofthe-money options explodes and compute a closed-form high-order expansion detailing the rate of the explosion. Furthermore the result shows that the square-root behaviour of the variance process induces a singularity such that for certain parameter configurations one cannot obtain high-order out-of-the-money forward smile asymptotics. In the at-the-money case a separate model-independent analysis shows that the small-maturity limit is well defined for any Itô diffusion. The proofs rely on the theory of sharp large deviations (and refinements) and incidentally we provide an example of degenerate large deviations behaviour.

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تاریخ انتشار 2013