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FRM Part II · FRM Exam Part II · The Financial Stability Implications of Artificial Intelligence

A bank uses three AI vendors for critical functions. Each vendor independently has a 2% probability of a severe outage in a year. Vendor A and B both run on the same cloud provider, which has a 1% annual probability of an outage that takes down both A and B (assume this is the only link and that other outage events are independent of it and of each other; ignore overlap of the cloud event with vendor-specific events when computing approximate figures, using P(A and B both down) ≈ P(cloud) + P(A)P(B)). What is the approximate probability that both A and B are down simultaneously, and how does it compare with the independent case?

The joint outage probability is about 1.04%, from the 1% shared cloud failure plus 0.04% independent overlap (2% × 2%). That is 26 times the 0.04% implied by independence, showing how a shared upstream provider sharply raises correlated failure risk.

  1. A0.04%, the same as the independent case
  2. B1.04%, about 26 times the independent case of 0.04%Correct
  3. C2.00%, about 50 times the independent case
  4. D1.00%, equal to the cloud probability only

Explanation

Independent case: 0.02 × 0.02 = 0.0004 = 0.04%. With the common cloud link: 0.01 + 0.0004 = 0.0104 = 1.04%. The ratio is 1.04/0.04 = 26. Ignoring the common dependency (option A) understates joint failure by a factor of 26; option D omits the independent component.

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