Before revision: We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility smile in a large class of models, including Heston and time-changed exponential Levy models.
After revision: We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility smile in a large class of models, including the Heston stochastic volatility and time-changed exponential Levy models.