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FRM Part II · FRM Exam Part II · VaR Mapping

A bank's options book is hedged so that its net delta is zero. The risk manager reports a delta-normal VaR that is close to zero, even though the book holds large long and short positions in straddles with different strikes. What is the main weakness of this VaR figure?

The delta-normal VaR understates risk. It captures only linear price exposure, so a delta-neutral book looks riskless. The book still carries gamma risk from large price moves and vega risk from changes in implied volatility, which full revaluation or higher-order mapping would capture.

  1. AIt overstates risk because delta hedging removes all exposure to volatility changes
  2. BIt understates risk because it ignores gamma and vega exposures that remain after the delta hedgeCorrect
  3. CIt is correct because a zero-delta book has no market risk
  4. DIt is unreliable only because delta-normal VaR cannot use volatility estimates

Explanation

Delta-normal mapping captures only first-order exposure to the underlying price. A delta-neutral options book can still lose from large price moves (gamma) and from changes in implied volatility (vega). A figure near zero therefore understates risk. Full revaluation or a delta-gamma-vega approach is needed.

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