The implied volatility of Forward-Start options: ATM short-time level, skew and curvature

Authors: Elisa Alòs, Antoine Jacquier and Jorge A. León

Stochastics, Vol. 91, No 1, 37-51, January, 2019

Using Malliavin Calculus techniques, we derive closed-form expressions for the at-the-money behaviour of the forward implied volatility, its skew and its curvature, in general Markovian stochastic volatility models with continuous paths.

This paper originally appeared as Barcelona GSE Working Paper 988