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

Figures & data

Figure 1. Illustration of the term structure of implied volatility of the Modified Rough Bergomi model in the Moderate deviations regime with time-varying log-strike $k_t=0.4t^{\beta }$. Depicted are the asymptotic formula (equation (17(17) ${\sigma }_{\mathrm{impl}}(k_t,t)={\sigma }_0+\rho \frac{{\sigma }_0^{\mathrm{\prime }}}{{\sigma }_0}⟨K1,1⟩k{t}^{\beta }+\mathcal{O}\left({\phi }_{3,H,\beta ,\theta }\right(t\left)\right).$(17) ), dashed line) and an estimate based on $N={10}^8$ samples of a MC Cholesky Option Pricer (solid line) with 500 time steps. Model parameters are given by spot vol ${\sigma }_0\approx 0.2557$, vvol $\eta =0.2928$ and correlation parameter $\rho =-0.7571$.