MTH305 RISK MANAGEMENT 1st SEMESTER 2021/22 FINAL EXAMINATION
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1st SEMESTER 2021/22 FINAL EXAMINATION
BACHELOR DEGREE – Year 4
MTH305
RISK MANAGEMENT
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Problem Solving – Excel Work (100 marks) Please attempt all the following problems using the given Excel template on the learning mall. |
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Q1 |
Suppose we back-test a VaR model using 800 days of data. If the VaR model used is accurate, the probability of the VaR being exceeded on any given day is p. We can consider two alternative hypotheses: H0 : The probability of an exception on any given day is p. H1 : The probability of an exception on any given day is greater than p. From the properties of the binomial distribution, the probability of the VaR level being exceeded on m and more days is
∑k(n)=m k!( The VaR confidence level is 99% and we observe 10 exceptions. 1) Calculate the expected number of exceptions. [2 marks] 2) Using the BINOMDISTfunction in Excel, calculate the probability of 10 or more exceptions. [5 marks] 3) At a 5% significant level, should we accept or reject the VaR model? [3 marks] |
10 marks |
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Q2 |
Table 1 Annual Default Ratesfor All Rated Companies, 1975-1996
SOURCE: Moody’s. |
18 marks |
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Table 1 shows the default ratesfor all rated companies in the US between 1975 and 1996. If a company defaults, its loans will default as well. Based on the one- factor Gaussian copulafor a portfolio of loans, wefind that the probability densityfunctionfor default rate is
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2023-01-06