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FRM Part II · FRM Exam Part II · VaR Mapping

A desk is short options on 20,000 shares of a stock. Per share, the net position has a delta of +0.10 and a gamma of -0.80. A risk analyst defines the 99% worst-case price move as either +$5 or -$5 and uses a delta-gamma approximation to value the position. What is the 99% loss estimate over the horizon?

The 99% loss estimate is $210,000. Negative gamma costs $10 per share for a $5 move in either direction. A fall adds a further $0.50 loss from the positive delta, so the worst case is $10.50 per share, or $210,000 over 20,000 shares.

  1. A$190,000
  2. B$200,000
  3. C$210,000Correct
  4. D$410,000

Explanation

Per share, the gamma term is 0.5 × (-0.8) × 25 = -10 for either move. For a +$5 move, the delta term is +0.5, so the change is -9.5. For a -$5 move, the delta term is -0.5, so the change is -10.5. The worst case is -10.5 × 20,000 = -$210,000. Using the up move gives $190,000. Ignoring delta gives $200,000. Omitting the one-half factor gives $410,000.

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