Suppose that from historical simulation, you have obtained n = 500 loss scenarios, the following table contains the five worst loss scenarios and the estimated daily volatilities. Scenario Loss ('000s) 494 477.841 339 345.435 349 282.204 329 277.041 487 253.385 ; (bps) 129.1 102.2 128.6 93.8 102.0 a) Assume each scenario is equally likely, find the one-day 99% value-at-risk (VaR) and expected shortfall (ES). (1 mark) b) Assume exponential weighting, that is, the weight for scenario i is given by An- (1-X)/(1-A"), where = 0.99. Find the one-day 99% VaR and ES. (2 marks) c) Suppose that we have estimated the daily volatility ; for each scenario i, and the current volatility is estimated to be an+1 = 206.4 basis points (bps) per day. Find volatility-adjusted losses for each scenario, then calculate the one-day 99% VaR and ES. Assume exponential weighting for each scenario. (2 marks) d) Suppose we back-test the one-day 99% VaR and observe 10 exceptions. Should we reject the model at the 5% significance level? Use Kupiec's two-tailed test. (1 mark)