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

A bank's model maps a portfolio of options to delta-equivalent positions in the underlying and uses a parametric normal VaR at 99%. The portfolio is short gamma. The underlying's daily volatility is 2%, position delta-equivalent exposure is USD 50 million. Delta-normal VaR (z=2.33) is closest to which value, and how does the short gamma affect the true VaR?

Delta-normal VaR is 2.33 × 2% × USD 50 million = USD 2.33 million. Because the book is short gamma, large moves cause losses beyond the linear approximation, so the true VaR is likely higher than this figure.

  1. AUSD 1.17 million; true VaR is likely higher
  2. BUSD 2.33 million; true VaR is likely higherCorrect
  3. CUSD 2.33 million; true VaR is likely lower
  4. DUSD 1.17 million; true VaR is likely lower

Explanation

Delta-normal VaR = 2.33 × 2% × 50m = 2.33m. A short gamma position loses on large moves in either direction, so the linear approximation understates the loss; true VaR is higher. Option with 1.17m wrongly halves the value (e.g. using 1% volatility).

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