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FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"

A risk manager compares two long option positions on the same stock with the same strike: Option A expires in one week and Option B in one year, both at-the-money. Which statement about their gammas is correct?

The one-week at-the-money option has higher gamma than the one-year option. As expiry approaches, delta of an at-the-money option becomes extremely sensitive to small stock price moves, so gamma rises sharply while it stays positive for long positions.

  1. AOption A has a lower gamma than Option B
  2. BOption A has a higher gamma than Option BCorrect
  3. CBoth have equal gamma because strikes are equal
  4. DOption A has negative gamma because of faster time decay

Explanation

At-the-money gamma rises as maturity shortens, because delta shifts sharply from near 0 to near 1 around the strike. Thus the one-week option has the higher gamma. Gamma is positive for all long options, so the last choice is wrong.

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