The power law in operational risk modeling states that for a random variable v and a high value x:

Pr(v > x) ≈ Kx^(-α)

Where:

• Pr denotes probability
• K and α are parameters

Key characteristics:

• Only describes the right tail - The power law applies to extreme events in the tail of the distribution, not the entire distribution
• Approximately true for high values - The relationship holds more accurately for larger values of x
• Used for extreme value theory - Particularly useful for modeling rare but severe operational losses

Why other options are incorrect:

• A: Operational losses do not follow normal distribution; they typically have heavy tails
• B: Power law has been successfully applied to natural disasters (earthquakes, floods)
• C: Power law models tail events, not losses in the body of the distribution