Here are two questions related to implied volatilities.
a) The set up here is for an European option. We can get its implied volatility smile from calibration, the question is why could we also observe 'volatility smile' in the market?
b) The second question is for the Heston stochastic volatility model. We use the Heston model to calibrate the implied volatilities of an European option for short term and long term maturities. The results shows clearly it is better fit with long maturity. Why? (Here the Heston model implied volatilities are plotted against the market implied volatilities)
The full answer is not necessarily needed here, some indications or references can also help.