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FRM Part II · FRM Exam Part II · VaR Mapping

A desk is short an at-the-money straddle (a short call and a short put with the same strike). The position's net delta is approximately zero. A risk manager computes VaR using delta-normal mapping. Which statement best describes the result?

Delta-normal VaR would be close to zero and would understate risk. A short straddle has near-zero delta but strongly negative gamma, so large price moves in either direction cause losses. A linear delta mapping ignores this curvature.

  1. AVaR is close to zero and understates risk, because the position has substantial negative gammaCorrect
  2. BVaR is accurate, because a zero delta means the position has no market risk
  3. CVaR is overstated, because the position has positive gamma
  4. DVaR is overstated, because the position has negative vega

Explanation

Delta-normal mapping captures only the linear exposure. With zero delta, the mapped VaR is near zero. A short straddle has large negative gamma, so large moves in either direction produce losses that the linear approximation misses. It therefore understates risk.

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