Skip to content

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

A dealer has sold 4,000 call options (delta 0.50, gamma 0.04 per option) and is delta-hedged with shares. The dealer wants to become both delta- and gamma-neutral using a traded option with delta 0.40 and gamma 0.08. Which action is required?

Buy 2,000 traded options and sell 800 shares. The short calls have gamma of -160, which requires 160/0.08 = 2,000 long options. Those options add delta of +800, so the dealer must sell 800 shares to bring the net delta back to zero.

  1. ABuy 2,000 of the traded options and sell 800 sharesCorrect
  2. BBuy 2,000 of the traded options and buy 800 shares
  3. CBuy 8,000 of the traded options and sell 3,200 shares
  4. DSell 2,000 of the traded options and buy 800 shares

Explanation

Short gamma = -4,000(0.04) = -160. Need +160 from the traded option: 160/0.08 = 2,000 options bought. These add delta 2,000(0.40) = +800, so sell 800 shares to restore delta neutrality. Buying 800 shares would add to the delta instead of offsetting it.

Did you get it right without looking?

One question tells you little. A timed set on Option Sensitivity Measures: The "Greeks" shows your real accuracy, how long you take and where you lose marks.

Practise Option Sensitivity Measures: The "Greeks"Free diagnostic mock

More Option Sensitivity Measures: The "Greeks" questions