Required file : Create implied volatility smile

Here we see how a local volatility model predicts the smile curve when the forward price is chaged. We first create a local volatility model using current F and obtain implied volatility smile from the local volatiltiy surface.
Let's see what happens when F moves down. We use the old local volatility surface but only change F. The implied volatility smile is shown as blue curve in the below figure:


As can be seen by looking at the blue curve, the smile has moved to the right when F is decreased. However, it is observed in market that smile actually moves in the same direction as F. This is thus clearly wrong.
Similarly, the red curve shows the smile when F is increased. This also moves in opposite direction and contradicts actual behaviour.
This weakness of predicting wrong dynamics in local volatility model has led to popularity of SABR model which overcomes this limitation.