Skip to content

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

A trader holds a long position in a call option on a stock. A risk analyst estimates 1-day VaR using the delta-normal approach, which approximates the option's value change using only delta. Compared with full revaluation, for a long call position the delta-only VaR estimate will typically be:

Delta-only VaR for a long call is typically overstated. The call has positive gamma, so its true value curve is convex and lies above the delta tangent line. Actual losses from adverse moves are smaller than the linear approximation suggests, so full revaluation gives a lower VaR.

  1. AOverstated, because the long call has positive gamma and the delta approximation ignores the cushion of convexityCorrect
  2. BUnderstated, because the delta approximation ignores the positive theta of the option
  3. CUnderstated, because the long call has negative gamma
  4. DIdentical, because delta fully captures option price changes for small moves

Explanation

A long call has positive gamma, so its true value curve lies above the tangent line given by delta. Losses on a price fall are smaller under full revaluation than under the linear approximation, so delta-only VaR overstates the loss. Option C has the wrong sign of gamma; D is only true for infinitesimal moves.

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