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

A trader uses a volatility surface where implied volatility is tabulated by strike and maturity. She needs to price a 5-month option whose strike lies between tabulated strikes, and no 5-month column exists, only 3-month and 6-month. What is the standard practitioner approach?

The standard approach is to interpolate implied volatility between the tabulated strikes and maturities on the surface, then plug that interpolated volatility into Black-Scholes-Merton. This respects both smile and term structure information, unlike using only the nearest maturity or historical volatility.

  1. AInterpolate implied volatility across both strike and maturity dimensions, then input the interpolated volatility into the Black-Scholes-Merton modelCorrect
  2. BUse the 6-month volatility at the same strike because it is the nearest maturity
  3. CAverage the premiums from the two surrounding maturities without reference to volatility
  4. DUse historical volatility over the past 5 months instead of the surface

Explanation

The surface is used to read implied volatility for non-tabulated strikes and maturities by interpolation, and the result is used in the pricing model. Using the nearest column ignores term structure information, and historical volatility is not the market-implied input.

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