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

A dealer faces a counterparty under a daily-margined CSA with zero threshold. The dealer's exposure model uses a margin period of risk (MPOR) of 10 business days. Daily exposure volatility is USD 1 million and exposure changes are i.i.d. normal. Assuming no initial margin, the 99% one-sided quantile is 2.33. After a review, the dealer concludes disputes will lengthen MPOR to 20 business days. Approximately what is the new 99% potential uncollateralised exposure, and by what factor does it rise?

With i.i.d. normal changes, exposure scales with the square root of the margin period of risk. The new figure is 2.33 times 1 million times the square root of 20, about USD 10.4 million. It rises by the square root of two, roughly 1.41, not doubling.

  1. AAbout USD 10.4 million; factor of about 1.41Correct
  2. BAbout USD 6.9 million; factor of about 1.41
  3. CAbout USD 10.4 million; factor of 2.0
  4. DAbout USD 9.3 million; factor of about 1.41

Explanation

Under square-root-of-time scaling, exposure = 2.33 x 1 x sqrt(20) = 2.33 x 4.472 = 10.42 million. The old value is 2.33 x sqrt(10) = 7.37 million, so the factor is sqrt(2) = 1.41. Doubling the factor ignores the square-root scaling. USD 6.9 million and 9.3 million do not correspond to a consistent calculation with the stated inputs.

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