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

A trader notes that for a commodity option, implied volatility rises as the strike price rises. Which implied risk-neutral distribution is consistent with this pattern, compared with a lognormal distribution?

An upward-sloping implied volatility pattern across strikes corresponds to a heavier right tail and thinner left tail than the lognormal. High-strike options are relatively expensive because large price rises are assigned greater probability, as is typical in some commodity markets.

  1. AHeavier right tail and thinner left tailCorrect
  2. BHeavier left tail and thinner right tail
  3. CSymmetric with thinner tails
  4. DIdentical to the lognormal distribution

Explanation

Rising implied volatility with strike means high-strike calls are relatively expensive, indicating more probability of large upward moves, a heavier right tail. Low-strike options are relatively cheap, implying a thinner left tail. This is the reverse of the equity skew.

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