The new standardized approach for determining a bank's operational risk capital requirements is based on two components: a measure of a bank's income and a measure of a bank's historical losses. It assumes that banks which have a history of operational risk losses are more likely to experience operational risk losses in the future. This is because past performance is often a good indicator of future performance, especially when it comes to operational risk. Banks that have experienced operational risk losses in the past have demonstrated that they have vulnerabilities in their operations that can lead to losses. These vulnerabilities may be due to a variety of factors, such as inadequate internal controls, poor risk management practices, or a lack of effective oversight. Unless these issues are addressed, the bank is likely to continue experiencing operational risk losses in the future. Therefore, the assumption that banks with a history of operational risk losses are more likely to experience such losses in the future is a key component of the new standardized approach for determining operational risk capital requirements.

Choice A is incorrect. The new standardized approach for calculating a bank's operational risk capital requirements does not assume that the operational risk escalates at a diminishing rate as the bank's income increases. Instead, it assumes that the operational risk increases proportionally with the increase in income.

Choice C is incorrect. As explained above, assumption I is not correct under the new standardized approach for calculating a bank's operational risk capital requirements. Therefore, both assumptions I and II cannot be correct.