FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces
A trader uses a volatility surface to price a European option with a 9-month maturity. Quoted implied volatilities at the same strike are 22% for 6 months and 26% for 12 months. Using linear interpolation in maturity on implied volatility, what volatility should be used?
The 9-month volatility is 24%. Nine months lies midway between 6 and 12 months, so linear interpolation gives the average of 22% and 26%, which is 24%.
- A24%Correct
- B23%
- C25%
- D24.5%
Explanation
9 months is halfway between 6 and 12 months. Linear interpolation gives 22% + 0.5 x (26% - 22%) = 24%. Using 23% would weight the short end at 75%, and 25% would weight the long end at 75%.
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