FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces
A risk manager observes that equity index options show a pronounced downward-sloping implied volatility skew for one-month maturities that flattens markedly at two-year maturities. Which model feature most directly explains a skew that is steep at short maturities and fades with longer maturities?
Jumps in the asset price explain it. Jumps create heavy tails and skew over short horizons, but over longer maturities their effect is diluted as returns aggregate toward a more normal distribution, so the implied volatility smile flattens as maturity increases.
- AConstant elasticity of variance with a very small exponent
- BJumps in the asset price, whose effect on the return distribution is diluted over longer horizonsCorrect
- CA deterministic volatility that rises with the time to maturity
- DA higher risk-free rate in the pricing model
Explanation
Jump processes create large non-normal moves over short horizons, producing steep smiles. Over longer horizons the sum of many small diffusive moves and jumps tends toward normality by the central limit theorem, so the smile flattens. The other options do not generate a short-dated skew that fades with maturity.
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