Dr. Blanka Horvath

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 (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 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 (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