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

A desk is short a large position in out-of-the-money call options, so its portfolio has negative gamma. A risk manager compares delta-normal VaR with VaR from full revaluation for large moves in the underlying. Which statement is most accurate?

Delta-normal VaR tends to understate risk for a short-option, negative-gamma book. The linear approximation ignores the convexity term, which is a loss for large moves in either direction. Full revaluation or a delta-gamma adjustment captures these losses, and the gap widens as the move grows.

  1. ADelta-normal VaR tends to understate the risk because it ignores the negative convexity losses.Correct
  2. BDelta-normal VaR tends to overstate the risk because it ignores the positive convexity gains.
  3. CDelta-normal VaR equals full-revaluation VaR because the delta is unchanged over one day.
  4. DDelta-normal VaR is accurate for large moves but inaccurate for small moves.

Explanation

With negative gamma, the second-order term 0.5 x gamma x dS^2 is a loss for moves in either direction. A linear delta approximation omits it, so potential losses are understated, and the error grows with the size of the move. The overstatement case applies to long-gamma positions.

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