FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces
A risk manager notes that as the equity option maturity increases, the volatility smile for the index typically becomes less pronounced. Which statement best describes this feature of volatility surfaces?
Volatility smiles typically flatten as maturity lengthens, so the surface is steeper across strikes for short-dated options. Longer horizons average out return shocks, making the distribution closer to lognormal, though the smile does not vanish completely.
- AThe smile flattens with longer maturity, so the surface is steeper in strike at short maturitiesCorrect
- BThe smile steepens with longer maturity, so the surface is steeper in strike at long maturities
- CThe smile is independent of maturity under stochastic volatility
- DThe smile disappears entirely beyond one year for all assets
Explanation
Empirically, smiles and skews are most pronounced for short maturities and flatten as maturity grows, partly because of averaging of return distributions over time. The disappearance beyond one year is too extreme, and independence of maturity is not observed.
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