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

A call option is worth USD 8.00 with the stock at USD 100. Its delta is 0.60 and gamma is 0.02. A full revaluation after the stock falls to USD 95 gives an option value of USD 5.20. How does the delta-gamma estimate of the loss per option compare with the full revaluation loss?

The delta-gamma estimate is a loss of USD 2.75 per option, while full revaluation shows a loss of USD 2.80. The approximation therefore understates the loss by USD 0.05, because it ignores higher-order terms beyond gamma.

  1. AIt estimates a loss of USD 2.75, understating the full revaluation loss by USD 0.05Correct
  2. BIt estimates a loss of USD 2.75, overstating the full revaluation loss by USD 0.05
  3. CIt estimates a loss of USD 3.00, overstating the full revaluation loss by USD 0.20
  4. DIt estimates a loss of USD 2.75, understating the full revaluation loss by USD 0.25

Explanation

Delta-gamma change = 0.60 × (−5) + 0.5 × 0.02 × 25 = −3.00 + 0.25 = −2.75. Full revaluation loss = 8.00 − 5.20 = 2.80. The approximation therefore understates the loss by 0.05, as higher-order terms are ignored. The 3.00 figure is the delta-only estimate, which would overstate by 0.20.

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