Short-time near-the-money skew in rough fractional volatility models. Issue 5 (4th May 2019)

• Record Type: Journal Article
• Authors: Bayer, C.; Friz, P. K.; Gulisashvili, A.; Horvath, B.; Stemper, B.
• Is Part Of: Quantitative finance. Volume 19:Issue 5(2019)
• Page Start: 779
• Page End: 798
• Publication Date: 2019-05-04
• Subjects: Rough stochastic volatility model -- European option pricing -- Small-time asymptotics -- Moderate deviations; 91G20 -- 60H30 -- 60F10 -- 60H07 -- 60G22 -- 60G18; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2018.1529420
• Languages: English
• ISSNs: 1469-7688

Abstract

Abstract : We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the 'rough' regime of Hurst parameterH < 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 ordert 1 / 2 (works of Alòs, León & Vives and Fukasawa) to the wider moderate deviations regime.