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

A market maker hedges a long position in short-dated at-the-money options. After a sudden jump in the underlying, realized gamma P&L is lower than expected from the Black-Scholes gamma. Which feature of the volatility surface best explains why gamma computed from a flat-volatility model may misstate gamma risk for short-dated options?

Smiles are typically steeper at short maturities, so implied volatility changes noticeably with strike and the underlying price. This changes the effective curvature of option value, meaning a flat-volatility Black-Scholes gamma can misstate gamma risk for short-dated options.

  1. AShort-dated implied volatility is always lower than long-dated implied volatility
  2. BShort-dated smiles are typically more pronounced, so the curvature of option value with respect to the underlying differs from the flat-volatility valueCorrect
  3. CGamma depends only on the risk-free rate
  4. DSmile effects vanish as expiry approaches

Explanation

Smiles and skews are typically more pronounced for short maturities, so implied volatility varies significantly with strike and the underlying. This alters the effective curvature of option value, so flat-volatility gamma misstates gamma risk. Smile effects do not vanish near expiry; they tend to be strongest there.

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