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

A trader holds a long position in a European call option on a non-dividend-paying stock. Holding other factors constant, which statement best describes the option's gamma?

Long European calls have positive gamma, meaning delta rises as the underlying price rises. Gamma measures the rate of change of delta, and the call's delta moves from near zero to near one as the option becomes more in the money, so it is not constant.

  1. AGamma is positive, so the option's delta increases as the stock price risesCorrect
  2. BGamma is negative, so the option's delta decreases as the stock price rises
  3. CGamma is positive, so the option's delta decreases as the stock price rises
  4. DGamma is zero because a call's delta is constant between 0 and 1

Explanation

Gamma is the second derivative of option value with respect to the stock price, i.e. the rate of change of delta. For long calls (and long puts) gamma is positive, so delta rises as the stock price rises. The option's delta is not constant; it moves from near 0 to near 1 as the option goes from out of the money to in the money.

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