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

A risk manager observes that implied volatilities for short-dated equity index options show a pronounced skew, with low-strike puts carrying much higher implied volatility than at-the-money options. Which feature of the underlying return distribution, relative to the lognormal assumption, is most consistent with this pattern?

A downward-sloping equity skew, with low-strike puts priced at higher implied volatility, indicates the market-implied distribution has a heavier left tail than the lognormal. Investors pay more for downside protection, so extreme falls are assigned more probability than the Black-Scholes model assumes.

  1. AA heavier left tail than the lognormal distributionCorrect
  2. BA heavier right tail than the lognormal distribution
  3. CA lighter left tail and a heavier right tail
  4. DIdentical tails but a higher mean return

Explanation

Higher implied volatility for low strikes means the market assigns more probability to large downward moves than the lognormal model does. That corresponds to a heavier left tail. A heavier right tail would produce higher implied volatility for high strikes, as seen in some currency or commodity smiles.

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