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FRM Part II · FRM Exam Part II · Case Study: Model Risk and Model Validation

A bank prices a portfolio with a model whose key volatility parameter is uncertain. Under a base volatility of 20% the portfolio is worth USD 50.0 million. Under 18% it is worth USD 47.5 million and under 24% it is worth USD 56.0 million. Management adopts a conservative approach: the model-risk adjustment is the difference between the base value and the lowest value across the plausible parameter range, and the adjusted value is the base value less this adjustment, with the position held as a long. What is the adjusted value?

The adjusted value is USD 47.5 million. For a long position the conservative case is the lowest valuation across the volatility range, which is 47.5 million, so the adjustment is 2.5 million deducted from 50.0 million. Using the higher value or adding the adjustment goes the wrong way.

  1. AUSD 47.5 millionCorrect
  2. BUSD 52.5 million
  3. CUSD 44.0 million
  4. DUSD 56.0 million

Explanation

For a long position, the worst case is the lowest value, USD 47.5 million. Adjustment = 50.0 - 47.5 = 2.5 million, so adjusted value = 50.0 - 2.5 = 47.5. USD 52.5 million adds the adjustment (wrong sign); 56.0 uses the highest value (wrong direction); 44.0 subtracts the 6.0 upside gap.

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