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

Equity options on a stock show an implied volatility curve with a pronounced skew. A risk manager wants to detect mispricing of a single option relative to the rest of the surface. Which approach is most consistent with the standard method?

The standard approach is to compare the option's implied volatility to a smooth volatility surface fitted to comparable strikes and maturities. Deviations from the surface suggest relative mispricing, whereas using one flat volatility would wrongly label every option on the skew as mispriced.

  1. ACompare its implied volatility with the level from a smooth surface fitted to other options at similar strikes and maturitiesCorrect
  2. BCompare its price with Black-Scholes using one flat historical volatility for all strikes
  3. CCompare its delta with that of the underlying stock
  4. DCompare its premium with the intrinsic value only

Explanation

Because the market uses different implied volatilities by strike and maturity, mispricing is judged relative to the fitted surface, not a single flat volatility. A flat-volatility comparison would flag every skewed option as mispriced. Intrinsic value ignores time value.

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