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

A bank's equity options desk is short a portfolio of out-of-the-money puts and calls on a stock. Black-Scholes vega for the whole book is computed with a parallel shift in implied volatility. The desk head notes that actual vega losses were larger than predicted during a market sell-off. Which explanation is most consistent with the volatility smile framework?

Surface moves are rarely parallel. In a sell-off the skew steepens and the term structure changes, so a single parallel-shift vega misses strike and maturity bucket exposures, which explains why actual vega losses exceeded the prediction.

  1. AVega is independent of strike, so parallel shifts always capture risk
  2. BVolatility surface moves are not parallel; the skew steepened and the term structure shifted, so exposures to individual strike and maturity buckets matteredCorrect
  3. CVega is zero for out-of-the-money options
  4. DImplied volatility is constant across maturities in a sell-off

Explanation

A single vega assumes a parallel shift of the entire surface. In sell-offs, the skew typically steepens and short maturities move more than long ones, so bucketed vega exposures matter. The other options are false: vega varies with strike and is positive for out-of-the-money options.

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