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

A risk analyst compares the implied distribution of an equity index extracted from option prices with a lognormal distribution having the same mean and standard deviation. Equity index options exhibit a volatility skew in which implied volatility falls as strike rises. Relative to the lognormal distribution, the implied distribution has:

The implied distribution has a heavier left tail and a thinner right tail than the lognormal. Falling implied volatility as strike rises means low-strike options are relatively expensive and high-strike options are relatively cheap, which reflects greater probability of large downward moves.

  1. AA heavier left tail and a thinner right tailCorrect
  2. BA heavier right tail and a thinner left tail
  3. CThinner tails on both sides
  4. DHeavier tails on both sides with no asymmetry

Explanation

A downward-sloping skew means low-strike options are priced with higher implied volatility than lognormal, so the left tail is heavier. High-strike options have lower implied volatility, so the right tail is thinner. Option B describes the currency-type skew where volatility rises with strike.

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