Exercise 2: i=0 i=1 Fl. = 5.5% To=5% i=2 72.6% T2.ud T2.du =5% FL.d=4.7% T2.44 =...

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Exercise 2: i=0 i=1 Fl. = 5.5% To=5% i=2 72.6% T2.ud T2.du =5% FL.d=4.7% T2.44 = 4.5% 2 EF5157 You have estimated the risk neutral interest rate tree for the continuously compounded interest rate as in the table above. There is equal risk neutral probability to move up or down the tree and each interval time represents 1 year, that is, A = 1. = 1. a) Compute the value of a non-callable bond with principal N 100, maturity i = 3, and annual coupon rate of 5.00%. b) Compute the value of a similar bond that is callable starting i = 1. c) Which of the two bonds is more expensive for investors? Why? 2. Consider a 2-year mortgage with annual payment, $30,000 face value, and a contin- uously compounded mortgage rate of 5.25%. a) If there is no prepayment, what is the annual payment? b) Given the annual payment, compute the principal and interest payment each period (i.e. i = 1 and i = 2). Also, compute the value of the mortgage without prepayment option along the tree. c) Compare the value of the mortgage at each node with the principal outstanding. What is the option value? When is it optimal to exercise the option? N.B.: You cannot exercise at i = 0. d) Compute the value of the mortgage with prepayment. What is the homeowner really paying? e) How would you calculate the duration of the mortgage? Give its value. Exercise 2: i=0 i=1 Fl. = 5.5% To=5% i=2 72.6% T2.ud T2.du =5% FL.d=4.7% T2.44 = 4.5% 2 EF5157 You have estimated the risk neutral interest rate tree for the continuously compounded interest rate as in the table above. There is equal risk neutral probability to move up or down the tree and each interval time represents 1 year, that is, A = 1. = 1. a) Compute the value of a non-callable bond with principal N 100, maturity i = 3, and annual coupon rate of 5.00%. b) Compute the value of a similar bond that is callable starting i = 1. c) Which of the two bonds is more expensive for investors? Why? 2. Consider a 2-year mortgage with annual payment, $30,000 face value, and a contin- uously compounded mortgage rate of 5.25%. a) If there is no prepayment, what is the annual payment? b) Given the annual payment, compute the principal and interest payment each period (i.e. i = 1 and i = 2). Also, compute the value of the mortgage without prepayment option along the tree. c) Compare the value of the mortgage at each node with the principal outstanding. What is the option value? When is it optimal to exercise the option? N.B.: You cannot exercise at i = 0. d) Compute the value of the mortgage with prepayment. What is the homeowner really paying? e) How would you calculate the duration of the mortgage? Give its value.