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FRM Part II · FRM Exam Part II · Validating Bank Holding Companies' Value-at-Risk Models for Market Risk

A validator assesses a bank's VaR for an options book that uses delta-only mapping of option positions to the underlying equity price. Which concern is the most important to report?

The key concern is that delta-only mapping ignores gamma and vega. Option payoffs are non-linear, so for large moves or changes in implied volatility the linear approximation can materially misstate potential losses, usually understating them for short option positions.

  1. ADelta mapping overstates risk for all market moves because it ignores time decay
  2. BDelta mapping ignores gamma and vega, so it can materially misstate risk for large moves and changes in implied volatilityCorrect
  3. CDelta mapping makes the model non-linear and therefore impossible to backtest
  4. DDelta mapping requires the use of a longer historical window

Explanation

A delta-only (linear) approximation ignores convexity (gamma) and exposure to implied volatility (vega), so for large underlying moves or volatility shifts the estimated loss can differ greatly from the true loss. It does not overstate risk in all cases, is linear not non-linear, and does not dictate window length.

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