This might seem like a dumb question.
When using a volatility model, stochastic for example, we try to calibrate it so that it fits the implied volatility smile given by the market, but why is this volatility smile so important ? What can we do with our calibrated smile afterwards ? I read here and there that we can reprice exotic products afterwards or interpolate to get an implied volatility for a strike that is not listed on the market, but can you give more detail ? If possible using SABR or any other model as an example ?