On the power law in a class of sandwiched Volterra volatility models
We have proposed a class of volatility models driven by a general additive Volterra noise and with an explosive drift, the solution of which is actually keeping in a sandwiched range. In this talk we review the properties and deepen the study of the sp-called power law. Indeed, the Sandwiched Volterra Volatility (SVV) model is able to reproduce the power-law behaviour of the at-the-money implied volatility skew, provided the correct choice of the Volterra kernel. To obtain this result, we assess the second-order Malliavin differentiability of the volatility process and investigate the conditions that lead to explosive behaviours in the Malliavin derivative. As a supplementary result, we also prove a general Malliavin product rule.
Area: CS30 - Fractional processes and Malliavin calculus for stochastic models (Enrica Pirozzi)
Keywords: Volatility models, Volterra type dynamics, fractional Brownian motion, Malliavin calculus