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

A bank's equity derivatives desk notes that implied volatility surfaces for single stocks often show a smile rather than the pronounced skew seen for equity indices. Which explanation is most consistent with the models for smiles?

Single stocks can jump either way on firm-specific news, so their return distributions have fairly symmetric heavy tails and produce a smile. Equity indices instead reflect crash fears and a negative price-volatility link, which produces a pronounced downward skew.

  1. ASingle stocks have strictly negative price-volatility correlation stronger than that of indices
  2. BIndividual stocks can jump up or down on firm-specific news, giving more symmetric tails, whereas index crashes are skewed to the downside through leverage and crash fearsCorrect
  3. CIndices have constant volatility while single stocks have stochastic volatility
  4. DSingle stock options are always European while index options are American

Explanation

Firm-specific events such as takeovers or earnings surprises can produce large moves in either direction, producing more symmetric tails and a smile. Index returns show a stronger negative correlation with volatility and crash concerns, giving a skew. The other options misstate model or contract features.

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