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

A risk analyst at a bank observes that implied volatilities for at-the-money options on an equity index are 22% for 1-month expiry, 20% for 6-month expiry and 19% for 2-year expiry. Which statement best describes this volatility term structure and its typical interpretation?

The term structure is downward sloping because implied volatility declines with maturity. This typically happens when current short-term volatility is high compared with its long-run average and is expected to mean-revert, so longer-dated options embed lower average expected volatility.

  1. AIt is downward sloping, which commonly occurs when current short-term volatility is high relative to its long-run mean and is expected to revertCorrect
  2. BIt is upward sloping, which commonly occurs when short-term volatility is below its long-run mean
  3. CIt is flat, indicating that volatility is expected to remain constant
  4. DIt is humped, indicating that volatility is expected to peak at six months

Explanation

Implied volatility falls as maturity increases (22%, 20%, 19%), so the term structure is downward sloping. Hull notes that when short-term volatility is historically high, it is expected to revert to the long-run mean, giving a downward-sloping term structure. An upward slope would arise when short-term volatility is low.

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