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, September 2018

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.