Exercise 1. a. The value of the non-callable bond is 100.13 and the value of the callable bond is 99.74. The non-callable bond is more expensive because it doesn't have the prepayment risk that the callable bond has. b. For the 2-year mortgage we have: i. The annual payment is 5,375.87. ii. See the following (the value of the mortgage is without prepayment: 1 = 0 2 Interest paid 0.00 497.14 254.60 Principal paid 0.00 4,878.73 5,121.27 Principal outstanding 10,000.00 5,121.27 0.00 Mortgage without 9,973.14 5,088.18 0.00 prepayment 5,129.05 0.00 0.00 iii. The option value is: 1= 0 2 Value of option 3.70 0.00 0.00 7.78 0.00 retired It is optimal to exercise in node (1,1), since the exercise value, 7.78, is higher than the wait value, 0.00. iv. The value of the mortgage with prepayment is: 1 = 0 2 Mortgage with 9,969.44 5,088.18 0.00 prepayment 5,121.27 0.00 retired The homeowner is compensating the lender for the time value of money and the prepayment risk. c. Duration for the mortgage is calculated by the following formula: 1 DE-P - X Plu - Pid = 1 5, 088.18 - 5, 121.27 X =0.4149 71,u - 1,d 9,969.44 5.5% - 4.7%