The implied volatility of Forward-Start options: ATM short-time level, skew and curvature. (arXiv:1710.11232v1 [q-fin.PR])

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.