Question

Suppose that loan losses (in $ millions) satisfy the power law with α=2 and K=4. a)...

Suppose that loan losses (in $ millions) satisfy the power law with α=2 and K=4. a) What is the probability that loan losses exceed $5 million? b) What is the probability that loan losses exceed $10 million? c) What is the probability that loan losses exceed $10 million conditional on loan losses exceeding $5 million?

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Answer #1

Solution :

loan losses (in $ millions) satisfy the power law with α=2 and K=4

a) What is the probability that loan losses exceed $5 million?

P(Losses > $5)=4 x 5-2 =4/25=0.16 (I.e. 16%)

b) What is the probability that loan losses exceed $10 million?

P(Losses > $10) =4 x (2 x $5)-2 0.16/4=0.04 (I.e., 4%)

c) What is the probability that loan losses exceed $10 million conditional on loan losses exceeding $5 million?

P(Losses > $ 10 | losses > $5)= P(losses > $10)/ P(losses > $5)=0.25 (I.e., 25%)

Note that in general , if the random variable L satisfies the power law, then for any constants K2> K1,
P(L > K2| L > K1) = P(L > K2)/P(L > K1) = (K2/ K1)-α

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