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

Which statement about gamma and the volatility smile is most accurate for a trader who hedges a portfolio of options using a single flat volatility?

Gamma depends on the volatility input, so using one flat volatility instead of each strike's implied volatility misstates gamma and the rebalancing needed. The error is most important near the money and in the wings. Long option positions still keep positive gamma.

  1. AGamma is independent of volatility, so the smile has no effect
  2. BGamma is highest for deep in-the-money options, so smile effects are concentrated there
  3. CGamma of near-the-money options is sensitive to the volatility used, so using a flat volatility rather than the strike-specific implied volatility misstates the gamma and the re-hedging needsCorrect
  4. DThe smile makes gamma negative for long option positions

Explanation

Black-Scholes gamma depends on volatility through d1 and the sigma-sqrt(T) denominator. Using a single flat volatility instead of each strike's implied volatility misstates gamma, particularly near the money and for wings. Long options always have positive gamma, and deep in-the-money options have low gamma.

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