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

A call option is initially at-the-money with delta near 0.5. Holding other inputs constant, as the option moves deep in-the-money close to expiry, which description of its delta and the delta's sensitivity to the stock price (gamma) is most accurate?

Delta approaches 1 and gamma approaches zero. A deep in-the-money call near expiry behaves like the stock itself, so its delta is nearly constant at 1, meaning it barely changes as the stock moves.

  1. ADelta approaches 1 and gamma approaches zeroCorrect
  2. BDelta approaches 1 and gamma becomes very large
  3. CDelta approaches 0 and gamma approaches zero
  4. DDelta approaches 0.5 and gamma is at its maximum

Explanation

A deep in-the-money call near expiry will almost surely be exercised, so it moves one-for-one with the stock and delta approaches 1. Delta is flat there, so gamma is close to zero. Gamma is very large only near the strike close to expiry.

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