The Implied Volatility of Forward-Start Options: ATM Short-Time Level, Skew and Curvature

Abstract

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.

Keywords: Forward-Start Options, Implied Volatility, Malliavin Calculus, Stochastic Volatility Models