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

A risk analyst at a bank wants to compare volatility smiles across options with different maturities and as the underlying price moves over time. Which way of characterizing the smile, as discussed in Hull, is best suited to this purpose?

Plotting implied volatility against K/S0 (or K/F0) is best, because moneyness-based axes keep the smile comparable and more stable when the underlying price changes, whereas a plot against the absolute strike shifts as spot moves.

  1. APlotting implied volatility against the strike price K
  2. BPlotting implied volatility against K/S0, the ratio of strike to current spotCorrect
  3. CPlotting implied volatility against the option premium
  4. DPlotting implied volatility against the option's time value only

Explanation

Hull notes that the smile can be expressed as implied volatility against K/S0 (or K/F0), which keeps the smile more stable as the asset price changes. A plot against the raw strike shifts whenever spot moves. Premium and time value are not standard smile axes.

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