Skip to content

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

A portfolio holds 1,000 long call options. Each option has delta 0.60 and gamma 0.04. The underlying stock falls by USD 4. Using the delta-gamma approximation, what is the change in the value of the portfolio?

The portfolio loses about USD 2,080. Per option, the delta effect is −2.40 and the gamma correction is +0.5 × 0.04 × 16 = +0.32, giving −2.08. Multiplied by 1,000 options, the loss is USD 2,080.

  1. A−USD 2,080Correct
  2. B−USD 2,400
  3. C−USD 2,720
  4. D−USD 1,760

Explanation

Per option, change = delta × dS + 0.5 × gamma × dS² = 0.60 × (−4) + 0.5 × 0.04 × 16 = −2.40 + 0.32 = −2.08. For 1,000 options the change is −USD 2,080. −2,400 is delta only; −2,720 subtracts the gamma term; −1,760 omits the 0.5 factor.

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