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

A risk manager wants to describe the volatility smile in a way that remains comparable as the underlying price moves over time. Which approach is the most appropriate way to characterize the smile?

Plotting implied volatility against K/S0 or delta, instead of absolute strike, is the better way to characterize a smile over time. These measures keep the curve's shape more stable when the underlying price moves, making comparisons across dates and underlyings more meaningful.

  1. APlot implied volatility against the ratio K/S0 (or delta) rather than against the absolute strike price KCorrect
  2. BPlot implied volatility against the absolute strike price K only, because it never changes with the spot
  3. CPlot the option premium against the strike price instead of implied volatility
  4. DPlot historical volatility against the time to maturity

Explanation

Defining the smile against K/S0 or delta keeps the shape relatively stable as spot changes, whereas the absolute-strike form shifts when the spot moves. Premium plots are not volatility smiles, and historical volatility versus maturity is unrelated to the smile across strikes.

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