FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces
Two options on the same asset have the same strike. The 6-month option has a higher total implied variance than the 12-month option (implied volatility squared times maturity). Assuming no other differences, which statement is correct?
A calendar spread arbitrage exists. At a given strike, total implied variance must not fall as maturity lengthens, since longer-dated options contain more time for variance to accumulate. A higher value at 6 months than at 12 months violates this no-arbitrage condition.
- AA calendar spread arbitrage exists, because total implied variance should not decrease as maturity increasesCorrect
- BNo arbitrage exists, because shorter-dated options always have higher volatility
- CThis is consistent with a normal term structure of volatility
- DThe result shows the smile is symmetric
Explanation
Total variance σ²T must be nondecreasing in maturity at a fixed strike (in forward-moneyness terms), otherwise a calendar spread arbitrage exists. A higher value at 6 months than 12 months breaks this. A downward-sloping volatility term structure is not itself a violation, but a falling total variance is.
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