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

Holding other inputs constant, for which European option is gamma generally greatest?

An at-the-money option very close to expiry has the greatest gamma. Its delta changes abruptly around the strike as maturity nears, while deep in- or out-of-the-money options have nearly constant delta and long-dated options have flatter delta profiles.

  1. AA deep in-the-money option with six months to expiry
  2. BA deep out-of-the-money option with one year to expiry
  3. CAn at-the-money option very close to expiryCorrect
  4. DAn at-the-money option with three years to expiry

Explanation

Gamma peaks for at-the-money options and rises sharply as expiry approaches, because delta switches rapidly from near 0 to near 1 around the strike. Deep in- or out-of-the-money options have delta near constant, hence low gamma, and long-dated at-the-money options have lower gamma than short-dated ones.

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