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QUESTION 2 a) The following information relates to a step-up coupon callable bond: 100.000 7.5 99.444 7.5 9.0197% 99.772 4.25 7.0053% 100.000 99.817 7.5 4.25 99.971 5.4289% 7.5 7.53 12% 102.082 3.500% 100.000 7.5 102.249 101.257 4.25 5.7354% 7.5 102:993 6.1660% 4.25 100.000 4.4448% 7.5 104.393 102.334 4.25 7.5 4.6958% 5.0483% 100.000 7.5 Today Year 1 Year 2 Year 3 Year 4 (Year 0) Additional information: 1. Step-up: 4.25% for year 1 and 2 and 7.50% for year 3 and 4. 2. Computed value: Coupon based on step-up schedule short-term rate (r) 3. The four-year step-up callable note pays 4.25% for two years and then 7.5% for two more years. This note is callable at par at the end of year 2 and year 3. It is assumed that the interest rate volatility is 10%. Required: Determine the value of the embedded call option.A man runs on Hampstead Heath twice a week. The average duration of one of his outings is 40 minutes with a standard deviation of 5 minutes. His average running time per week is 1 hour 20 minutes with a standard deviation of 4 minutes. Given that he ran for only 15 minutes on Monday, what is the expected duration of his Friday outing? An investor has a choice of three financial assets. The expected yields of these assets are given in the vector [0.04 0.03 0.05] and the variances and covariances of the yields are given in the matrix 3.29 -0.83 10-4 0.83 3.41 O 2.01 Derive expressions for the expected yield and variance of a portfolio con- taining AQ of the first asset and (1- )Q of the second asset, and ascertain whether there is any value of A such that the variance of this portfolio is less than the variance of an investment @ in the third asset.1. Give an account of the axioms of Boolean algebra and, in the process, compare them with the axioms of arithmetic. Let A and B be two events within the sample space S, for which P(S) = 1. Let Ac and Be be the complements of A and B respectively. Given that P(AUB) - 0.3 and P(An B) = 0.1, find P(B). 2. Show how Bayes' theorem is used to obtain the posterior likelihood of an hypothesis from the prior likelihood when an event has occured which throws some light on the hypothesis. Usually I wash the breakfast dishes before leaving for the office. If I do not do so, then my wife will do so nine times out of ten if she returns from work first; but there is only a one-in-ten chance that my children will do so if they return from school before I get home. This morning I failed to wash the dishes. Also my wife told me that there is a fifty-fifty chance that she would return later than me. When I returned home, I discovered that the dishes had been washed, and I could hear that my children were at home. What were the chances that my wife was also at home