I have a convegence issue on a monte-carlo simulating a local vol process. I examine convergence with respect to number of time steps, keeping the number of paths constant. I watched a couple of different smiles (more or less skewed, more or less kurtosed), and looked how the simulated (I use the Euler scheme) smiles behave when the number of timesteps increases : the smile actually gets lower.This is contrary to my intuition (you sample less the smile, so if it has positive curvature, you should miss some vol. Hence it should go up.)Does anyone has a (correct) intuition of this ?

erratum from the previous message : I mixed up local vol and smile (implied vol)...I have a convegence issue on a monte-carlo simulating a local vol process. I examine convergence with respect to number of time steps, keeping the number of paths constant. I watched a couple of different local vol (more or less skewed, more or less kurtosed), and looked how the simulated (I use the Euler scheme) smiles behave when the number of timesteps increases : the smile actually gets lower.This is contrary to my intuition (you sample less the local vol, so if it has positive curvature, you should miss some vol. Hence it should go up.)Does anyone has a (correct) intuition of this ?