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FRM Part II · FRM Exam Part II · Margin (Collateral) and Settlement

A CSA has daily remargining. After a counterparty stops posting collateral, the bank needs 3 days to recognise the default and call the last margin, and 7 further days to close out and replace the trades, so the margin period of risk is 10 business days. Portfolio daily exposure volatility is USD 2 million and changes are assumed i.i.d. normal with zero drift. Using the square-root-of-time rule, what is the 10-day exposure volatility?

The 10-day exposure volatility is about USD 6.32 million. Under i.i.d. changes with zero drift, volatility scales with the square root of time, so the daily USD 2 million is multiplied by √10, about 3.162, rather than by 10.

  1. AUSD 6.32 millionCorrect
  2. BUSD 20.00 million
  3. CUSD 4.47 million
  4. DUSD 8.94 million

Explanation

Volatility scales with the square root of time: 2 × √10 = 2 × 3.162 = 6.32 million. USD 20 million wrongly scales linearly with time. USD 4.47 million uses √5, and USD 8.94 million uses √20.

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