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

A risk manager compares methods for a portfolio that is short a large number of options and so has substantial negative gamma, with a large possible market move. Which statement about the methods is correct?

For a book short options with negative gamma, full revaluation shows larger losses than delta-only for big moves. The value curve is concave and lies below the delta tangent, so the linear approximation understates risk. Revaluation captures this nonlinearity, giving a higher and more accurate VaR.

  1. AFull revaluation will generally show larger losses than delta-only for large adverse moves, because negative gamma makes the true loss exceed the linear estimateCorrect
  2. BDelta-only VaR will exceed full revaluation VaR, because short options always have positive convexity
  3. CDelta-gamma and delta-only give identical results whenever the position has any gamma
  4. DFull revaluation is less accurate than delta-only for large moves because it ignores second-order effects

Explanation

With negative gamma the value curve lies below its tangent, so large moves in either direction produce losses worse than the delta-only estimate. Full revaluation captures this, so delta-only understates VaR. The other options misstate convexity or the role of gamma.

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