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

A trader uses a local volatility model calibrated to today's implied volatility surface to hedge a barrier option. Two weeks later, spot has moved but the market surface has shifted in a different way than the model's forward dynamics implied. Which weakness of the local volatility model does this best illustrate?

The episode illustrates that local volatility models fit today's vanilla surface well but imply unrealistic future smile dynamics, typically a flattening smile. Hedges for path-dependent products such as barrier options can therefore perform poorly when the actual surface evolves differently from the model's forecast.

  1. AIt cannot be fitted to any vanilla option prices today
  2. BThe future smile it implies flattens unrealistically, so its dynamics of the smile are poor despite fitting today's surfaceCorrect
  3. CIt assumes volatility is constant across strikes and maturities
  4. DIt requires the underlying asset to follow a jump process

Explanation

A local volatility model can be calibrated to match today's vanilla prices exactly, so option A is wrong. However, the smile it predicts for the future tends to flatten and differ from observed evolution, making hedges for path-dependent products unreliable. It does not assume constant volatility, so option C is wrong.

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