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

A trader notes that for a given maturity, the implied volatility for a put with delta of -0.25 is 24%, the at-the-money option is 20%, and the call with delta 0.25 is 18%. Using the risk reversal and strangle (butterfly) conventions, with the strangle defined as the average of the 25-delta call and put volatilities minus the ATM volatility, and the risk reversal defined as call vol minus put vol, which pair is correct?

The risk reversal is -6% (18% call vol minus 24% put vol) and the strangle is +1% (the 21% average of the wing vols minus the 20% ATM vol), indicating a downside skew with some wing curvature.

  1. ARisk reversal = -6%; strangle = +1%Correct
  2. BRisk reversal = +6%; strangle = +1%
  3. CRisk reversal = -6%; strangle = -1%
  4. DRisk reversal = -3%; strangle = +21%

Explanation

Risk reversal = 18% - 24% = -6%. Strangle = (18% + 24%)/2 - 20% = 21% - 20% = +1%. Option B has the wrong sign on the risk reversal; C has the wrong sign on the strangle; D confuses averages and levels.

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