The volatility smile and skew, in full

the smile and skew

Why implied volatility varies across strikes: the smile (implied volatility higher for far-from-the-money strikes than at-the-money) and the skew (higher for downside strikes than upside in equities) reflect that real underlying returns are not the neat bell curve the simplest pricing assumes - they have fat tails and downside asymmetry, and the market prices that into the options. The skew is the market's memory of crashes, priced strike by strike.