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Article overview
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Small-time and large-time smile behaviour for the Rough Heston model | | Martin Forde
; Stefan Gerhold
; Benjamin Smith
; | | Date: |
21 Jun 2019 | | Abstract: | We characterize the asymptotic small-time and large-time implied volatility
smile for the rough Heston model introduced by El Euch, Jaisson and Rosenbaum.
We show that the asymptotic short-maturity smile scales in qualitatively the
same way as a general rough stochastic volatility model, and is characterized
by the Fenchel-Legendre transform of the solution a Volterra integral equation
(VIE). The solution of this VIE satisfies a space-time scaling property which
simplifies its computation. We corroborate our results numerically with Monte
Carlo simulations. We also compute a power series in the log-moneyness variable
for the asymptotic implied volatility, which yields tractable expressions for
the vol skew and convexity, thus being useful for calibration purposes. We also
derive formal asymptotics for the small-time moderate deviations regime and a
formal saddlepoint approximation for call options in the large deviations
regime. This goes to higher order than previous works for rough models, and in
particular captures the effect of the mean reversion term. In the large
maturity case, the limiting asymptotic smile turns out to be the same as for
the standard Heston model, for which there is a well known closed-form formula
in terms of the SVI parametrization. | | Source: | arXiv, 1906.9034 | | Services: | Forum | Review | PDF | Favorites | |
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