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FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces

Compared with a lognormal distribution having the same mean and standard deviation, the risk-neutral distribution implied by an equity index volatility skew has which feature?

The implied distribution has a heavier left tail and a lighter right tail than the lognormal. Out-of-the-money puts carry higher implied volatility, meaning more probability of large drops, while calls carry lower implied volatility, meaning less probability of large rises.

  1. AA heavier left tail and a lighter right tailCorrect
  2. BA heavier right tail and a lighter left tail
  3. CHeavier tails on both sides and no asymmetry
  4. DIdentical tails but a higher mean

Explanation

Low-strike options have higher implied volatility, so they are priced higher than under lognormality, which means more probability in the left tail. High-strike options have lower implied volatility, implying a lighter right tail. Option B reverses this relationship.

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