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

A dealer has sold 20,000 call options on a stock, each with delta 0.50 and gamma 0.04. The dealer is delta-hedged with shares. The stock price suddenly rises by $1. Using a delta-gamma approximation, what is the dealer's new unhedged delta exposure (in shares) before rebalancing?

The net delta becomes -800 shares. Gamma raises each call's delta to 0.54, making the short position worth -10,800 shares of delta, while the hedge holds only 10,000 shares, leaving the dealer 800 shares short.

  1. A-800 sharesCorrect
  2. B+800 shares
  3. C-10,800 shares
  4. D-1,000 shares

Explanation

Option delta rises to 0.50 + 0.04 = 0.54 per option. Short position delta changes from -10,000 to -10,800; the hedge holds +10,000 shares, so net delta = -800. The -1,000 option ignores the gamma scaling by position size incorrectly.

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