Short-time near-the-money skew in rough fractional volatility models

C. Bayer, P. K. Friz, A. Gulisashvili, B. Horvath, B. Stemper

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the ‘rough’ regime of Hurst parameter H < 1/2. This regime recently attracted a lot of attention both from the statistical and option pricing point of view. With focus on the latter, we sharpen the large deviation results of Forde-Zhang [Asymptotics for rough stochastic volatility models. SIAM J. Financ. Math., 2017, 8(1), 114–145] in a way that allows us to zoom-in around the money while maintaining full analytical tractability. More precisely, this amounts to proving higher order moderate deviation estimates, only recently introduced in the option pricing context. This in turn allows us to push the applicability range of known at-the-money skew approximation formulae from CLT type log-moneyness deviations of order t1/2 (works of Alòs, León & Vives and Fukasawa) to the wider moderate deviations regime.

Original languageEnglish
Pages (from-to)779-798
Number of pages20
JournalQuantitative Finance
Volume19
Issue number5
DOIs
StatePublished - 4 May 2019
Externally publishedYes

Keywords

  • European option pricing
  • Moderate deviations
  • Rough stochastic volatility model
  • Small-time asymptotics

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