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

An analyst compares two explanations of the volatility smile for options on a currency pair. Model A adds random jumps to the price process; Model B makes volatility stochastic. Which statement about their effects on the term structure of the smile is most accurate?

Jump models give smiles that are strongest at short maturities and flatten as maturity lengthens, because over long horizons the effect of occasional jumps is diluted and the return distribution moves closer to normal. Stochastic volatility smiles tend to persist longer.

  1. AJump models generate smiles that are most pronounced for short maturities and flatten as maturity increasesCorrect
  2. BJump models generate smiles that become steeper as maturity increases
  3. CStochastic volatility smiles are pronounced only for very short maturities, while jump smiles persist at long maturities
  4. DBoth models produce smiles that are independent of option maturity

Explanation

Jumps matter most over short horizons, since a single jump is a large share of total variance. Over longer horizons the many small diffusion moves and averaging make the distribution closer to normal, flattening the smile. Stochastic volatility effects accumulate and tend to persist at longer maturities, so the reverse in option C is wrong.

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