The following losses are ranked from highest to lowest for 500 scenarios in a historical simulation.

(a) The following losses are ranked from highest to lowest for 500 scenarios in a historical simulation. Suppose that three stress scenarios are considered. They lead to losses ($0005) 850 and 950. The probabilities assigned to the scenarios are 0.7% and 0.3%, respectively. The total probability of the stressed scenarios is, therefore 1%. Scenario L055 ('0005) 494 477.841 339 345.435 349 282.204 329 277.041 487 253.385 Assume exponential weighting is used (A : 0.99) for the historical scenarios. Compute the 1day 97.5% expected shortfall. (3 marks) (b) Suppose that we use MonteCarlo simulation to determine the loss distribution for operational risk. Moreover, the lossfrequency is modeled by the Poisson distribution with )i = 3.5 [average number of losses per year). i. Let n be the number of losses, calculate the probability for n = 0, n s 1 and n s 2, respectively. (2 marks) ii. If a random number between 0 and 1 is drawn, say 0.384, how many losses occurred in this simulation trial? (1 mark)