<t>Hello everyone!I have a question that I'm sure someone can help me with.Suppose that you have a convex function [$]\Phi(x)[$] and a stochastic process [$](X_t)_{t\geq 0}[$] that is a martingale: [$]\mathbb{E}[X_T|X_t]=X_t[$].Define [$]p(x)=\mathbb{E}[\Phi(X_T)|X_t=x][$]. I don't know how to show ...

<t>Hi,as I know, the VV is calibrated only on the 3 market quotes ATM, RR25, BF252vol, so you don't have the calibration to the full volatility smile/surface. On the other side, the LSV should be calibrated on the whole surface and a difference with the BS price can be seen as a calibration error IM...