FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces
A trader notes that a one-month GBP/USD option smile is quite pronounced while a five-year option smile on the same pair is much flatter. Which explanation is most consistent with the standard understanding of currency smiles?
Jump effects are most significant over short horizons and are diluted as maturity lengthens because cumulative returns move closer to normal. That is why the one-month smile is pronounced while the five-year smile is flatter. Dealer pricing conventions are not the reason.
- AJumps have a larger relative effect on short-dated options, and their impact diminishes as maturity increases because returns average out toward normalCorrect
- BLong-dated options are always priced with constant volatility by dealers
- CStochastic volatility has no effect at any maturity
- DInterest rate differentials dominate the smile only at short maturities
Explanation
With jumps, the effect on the return distribution is diluted over longer horizons as the sum of many small effects approaches normality, so the smile flattens with maturity. Stochastic volatility effects persist, though, which is why the smile does not fully vanish.
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