Interpret the volatility smile and skew

A model with one constant volatility implies the same implied volatility at every strike; markets disagree. A smile is a U shape, with deep in-the-money and out-of-the-money options carrying higher implied volatility than at-the-money ones, typical of currency options. A skew slopes: in equity index options implied volatility falls as the strike rises, because demand for crash protection makes out-of-the-money puts dearer than out-of-the-money calls. Adding maturity gives the volatility surface. A steep skew makes protective puts expensive, so a manager might part-fund protection by writing a lower-strike put, or use a risk reversal if expecting the skew to flatten. The mistake is calling the skew a mispricing; it prices tail risk.