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FRM Part II · FRM Exam Part II · Backtesting VaR

A bank's 99% one-day VaR shows 9 exceptions over 250 days. Investigation shows the VaR model prices an exotic option using a delta-only approximation, and exceptions occur on days with large market moves in either direction. What is the most likely cause?

The likely cause is omitted nonlinearity. A delta-only approximation ignores gamma, so for option positions large moves in either direction cause losses bigger than the linear estimate. VaR is understated on big-move days, producing exceptions. Full revaluation or a delta-gamma approach would improve the model.

  1. AOmission of nonlinear (gamma) risk causing underestimation of tail lossesCorrect
  2. BOverly long data window
  3. CUse of too high a confidence level
  4. DDaily rather than intraday data

Explanation

A delta-only approximation ignores convexity. For options positions, large moves in either direction produce losses larger than the linear estimate, so VaR is understated on big-move days. This is a model misspecification issue; the other options do not explain two-sided large-move exceptions.

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