What's a volatility smile? Why does it occur? What are the implications for Black Scholes?

Answer 1

The smile occurs when out of the money options are priced higher than the implied volatility of at the money options with the same maturity. Many times this is explained by the idea that there may be an abnormally large number of abnormally large changes in the returns of the underlying. This may be true, especially if Volatility is not constant. This may also arise simply because option users are risk averse. I would be happy to explain smiles and skew if you care! I have spent decades running option portfolios for banks and hedge funds.