Short-time near-the-money skew in rough fractional volatility models
研究了Hurst参数小于1/2的粗糙分数阶随机波动率模型，通过高阶中偏差估计改进了近价期权偏斜的近似公式，将适用范围从对数价格偏差阶数t^(1/2)扩展到更宽的中偏差区间。
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.