Skip to content

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

A call option is priced at $4.00 with the underlying at $50, delta 0.60 and gamma 0.05. The underlying falls to $46, and full revaluation gives a new option price of $2.20. How does the delta-gamma estimate of the loss compare with the full-revaluation loss?

The delta-gamma estimate overstates the loss by $0.20. It predicts a change of -2.40 + 0.40 = -$2.00, while full revaluation gives 2.20 - 4.00 = -$1.80. Higher-order terms not captured by gamma explain the remaining difference.

  1. AIt overstates the loss by $0.20Correct
  2. BIt understates the loss by $0.20
  3. CIt overstates the loss by $0.60
  4. DIt matches the full-revaluation loss exactly

Explanation

Delta-gamma change = 0.60 x (-4) + 0.5 x 0.05 x 16 = -2.40 + 0.40 = -2.00. The full-revaluation change is 2.20 - 4.00 = -1.80. The approximation shows a loss $0.20 too large. The delta-only loss of $2.40 would overstate by $0.60, which ignores gamma entirely.

Did you get it right without looking?

One question tells you little. A timed set on Calculating and Applying VaR shows your real accuracy, how long you take and where you lose marks.

Practise Calculating and Applying VaRFree diagnostic mock

More Calculating and Applying VaR questions