By means of Malliavin Calculus we see that the classical Hull and White formula for option pricing can be extended to the case where the noise driving the volatility process is correlated with the noise driving the stock ...

For stochastic volatility models, we study the short-time behaviour of the at-the-money implied volatility level, skew and curvature for forward-starting options. Our analysis is based on Malliavin Calculus techniques.