Skip to content

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

An equity index options desk observes that implied volatility falls steadily as the strike rises, for options of the same maturity. Compared with a lognormal distribution having the same mean and standard deviation, what is the implied risk-neutral distribution of the index at maturity?

A downward-sloping equity volatility skew implies a risk-neutral distribution with a heavier left tail and a thinner right tail than the lognormal. Low-strike options are priced richly, reflecting greater probability of large declines, while high-strike options are priced cheaply.

  1. AHeavier left tail and thinner right tailCorrect
  2. BHeavier right tail and thinner left tail
  3. CHeavier tails on both sides
  4. DThinner tails on both sides

Explanation

Decreasing implied volatility with strike means low-strike options (which pay off in the left tail) are relatively expensive, indicating a heavier left tail. High-strike options are relatively cheap, indicating a thinner right tail. The heavier-right-tail case describes the pattern seen in some commodity markets, which is the opposite.

Did you get it right without looking?

One question tells you little. A timed set on Volatility Smiles and Volatility Surfaces shows your real accuracy, how long you take and where you lose marks.

Practise Volatility Smiles and Volatility SurfacesFree diagnostic mock

More Volatility Smiles and Volatility Surfaces questions