The Probability of Operational Risk Losses Exceeding Certain Amounts
What is the probability of operational risk losses exceeding specific amounts?
Given that there is a 90% probability that operational risk losses will not exceed $20 million and the power law parameter, α, is 0.8, what is the probability of losses exceeding (a) $40 million, (b) $80 million, and (c) $200 million?
Calculating the Probability of Losses Exceeding Certain Amounts
The probabilities of losses exceeding $40 million, $80 million, and $200 million are approximately 0.4362, 0.0771, and 0.0002, respectively.
To find the probability of operational risk losses exceeding a certain amount, we can use the power law distribution formula:
P(x > k) = (k/α)^α
Where k is the threshold value and α is the power law parameter. In this case, the threshold values are $40 million, $80 million, and $200 million, and α is 0.8. Plugging in these values:
P(x > $40 million) = ($40/0.8)^0.8 ≈ 0.4362
P(x > $80 million) = ($80/0.8)^0.8 ≈ 0.0771
P(x > $200 million) = ($200/0.8)^0.8 ≈ 0.0002
This calculation shows that as the threshold value increases, the probability of operational risk losses exceeding that amount decreases significantly due to the nature of the power law distribution.