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FRM Part I · FRM Exam Part I · Calculating and Applying VaR

A trader is short 500 call options on a stock trading at USD 100. Each option has delta 0.50 and gamma 0.03. The risk manager's worst-case one-day move is USD 3 in either direction. Using the delta-gamma approximation, what is the worst-case loss on the position over the two scenarios?

The worst-case loss is USD 817.50, occurring when the stock rises USD 3. Per option the delta-gamma change is 1.50 + 0.135 = 1.635, and the short position loses that on 500 options. The USD 3 fall produces a gain, not a loss.

  1. AUSD 817.50Correct
  2. BUSD 750.00
  3. CUSD 682.50
  4. DUSD 885.00

Explanation

Short position P&L = −500 × (0.50 × dS + 0.5 × 0.03 × dS²). For dS = +3: −500 × (1.50 + 0.135) = −817.50. For dS = −3: −500 × (−1.50 + 0.135) = +682.50, a gain. The worst case is the loss of USD 817.50. USD 750 is delta only; USD 885 omits the 0.5 in the gamma term.

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