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

Under the Black-Scholes-Merton model, the risk-neutral distribution of the stock price is lognormal. Compared with this lognormal distribution, an implied distribution consistent with a typical equity volatility skew has which feature?

The implied distribution has a heavier left tail and a lighter right tail than the lognormal. High implied volatility at low strikes prices in a greater chance of large price falls, while low implied volatility at high strikes signals a thinner upside tail.

  1. AA heavier left tail and a lighter right tailCorrect
  2. BA lighter left tail and a heavier right tail
  3. CHeavier tails on both sides with equal weights
  4. DIdentical tails but a higher mean

Explanation

High implied volatility at low strikes means low-strike options are priced richer than lognormal, implying more probability of large declines. Low implied volatility at high strikes implies a thinner right tail. Option B describes the reverse skew.

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