We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the “rough” regime of Hurst pa- rameter 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 (2017) 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 es- timates, only recently introduced in the option pricing context. This in turn allows us to push the applicability range of known at-the-money skew approxi- mation formulae from CLT type log-moneyness deviations of order t1/2 (recent works of Alo`s, Le ́on & Vives and Fukasawa) to the wider moderate deviations regime.
This is work in collaboration with C. Bayer, P. Friz, A. Gulsashvili and B. Stemper
- Mathematical and Computational Finance Seminar