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

An analyst compares the implied distribution of an equity index derived from option prices with a lognormal distribution that has the same mean and standard deviation. The implied volatilities of the index options show a pronounced downward-sloping skew (higher volatility for low strikes). Relative to the lognormal distribution, the implied distribution will most likely have:

The implied distribution has a heavier left tail and a lighter right tail than the lognormal. High implied volatility at low strikes means out-of-the-money puts are expensive, so the market assigns more probability to large downward moves, which is the typical equity skew pattern.

  1. AA heavier left tail and a lighter right tailCorrect
  2. BA heavier right tail and a lighter left tail
  3. CLighter tails on both sides
  4. DIdentical tails, with differences only in the mean

Explanation

A downward-sloping equity skew means low-strike options are priced with higher volatility, so they are relatively expensive. This implies more probability in the left tail than a lognormal distribution and less in the right tail. The right-tail-heavy shape is typical of currency options with an upward skew, not equity.

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