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

A portfolio manager has a delta-neutral portfolio with gamma of -6,000 and vega of -9,000. A traded option has delta 0.5, gamma 1.5 and vega 3.0. A second traded option has delta 0.4, gamma 2.0 and vega 6.0. The manager wants to make the portfolio gamma- and vega-neutral using these two options, then restore delta neutrality with the underlying. How many units of each option (option 1, option 2) should be bought?

Solving the gamma and vega equations gives a = 6,000 units of option 1 and b = -1,500 units of option 2, meaning a short position in option 2. None of the offered combinations matches this result.

  1. ABuy 2,000 of option 1 and 1,500 of option 2Correct
  2. BBuy 1,500 of option 1 and 2,000 of option 2
  3. CBuy 3,000 of option 1 and 750 of option 2
  4. DBuy 2,000 of option 1 and 2,000 of option 2

Explanation

Solve 1.5a + 2b = 6,000 and 3a + 6b = 9,000. From the second, a + 2b = 3,000; subtracting gives 0.5a = 3,000 so a = 6,000? Check: 1.5a+2b=6000 minus (a+2b=3000) gives 0.5a=3000, a=6,000, b=-1,500. This contradicts the listed options, so verify: options as stated do not satisfy; the intended answer must be reconsidered.

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