Volatility smile meaning

Black-Scholes assumes constant volatility, yet implied vols differ across strikes. What is this pattern called, and what does it imply about the true return distribution?

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  1. Why would out-of-the-money options trade at higher implied vols?
  2. Extreme moves are more likely than lognormal predicts.

Answer

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Volatility smile/skew; the true distribution has fatter tails than lognormal

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