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

Implied total variance is sigma^2 times T. At-the-money implied volatility is 20% for a 1-year option and 22% for a 2-year option. Assuming the forward variance between years 1 and 2 is what links the two total variances, what is the implied forward volatility for that period, to the nearest 0.1%?

The forward volatility is about 23.8%. Total variance is 0.04 for one year and 0.0968 for two years, so forward variance for year two is 0.0568, whose square root is roughly 23.8%, higher than the 22% two-year spot volatility.

  1. A23.8%Correct
  2. B24.0%
  3. C22.0%
  4. D21.0%

Explanation

Total variance at 1 year = 0.04 x 1 = 0.04. At 2 years = 0.0484 x 2 = 0.0968. Forward variance = 0.0968 - 0.04 = 0.0568, so forward volatility = sqrt(0.0568) = 23.83%. Choosing 24.0% is a rounding approximation not matching the result, 22% ignores forwards, and 21% is the simple average.

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