bonds,

Valuation of callable bonds using binomial interest rate tree. You are interested in valuing several bonds. The binomial interest rate tree that describes the evolution of the annual interest rate and annual spot rates are given as follows: Binomial Interest Rate Tree Year 0 Year 1 Year 1 To = 3.5% 71,4 = 5.429% 71.d = 4.445% Year 2 r2uu = 7.005% 2.ud = 5.735% r2dd = 4.696% Year 3 3uuu = 9.199% 3.uud = 7.531% Tudd = 6.166% ryddd 5.048% Spot Rate 1-Year 3.5% 2-Year 4.2147% 3-Year 4.7345% 4-Year 5.2707% Assume that the risk-neutral probability that the annual interest rate moves up or down is 0.5 and par value is $100. 1. Value an option-free bond with four years to maturity using annual spot rates. The annual coupon rate is 6.5% and the coupon is paid annually (once at the end of each year). 2. Value a callable bond with four years to maturity using the binomial interest rate tree. The annual coupon rate is 6.5% and the coupon is paid annually (once at the end of each year). The bond is callable at every coupon payment date. 3. What is the value of the call option embedded in the above callable bond? 4. Value a callable bond with four years to maturity and a two-year call protection period (callable at the end of the second and third years). The coupon rate is 6,5% per period and the coupon is paid once at the end of every period. Valuation of callable bonds using binomial interest rate tree. You are interested in valuing several bonds. The binomial interest rate tree that describes the evolution of the annual interest rate and annual spot rates are given as follows: Binomial Interest Rate Tree Year 0 Year 1 Year 1 To = 3.5% 71,4 = 5.429% 71.d = 4.445% Year 2 r2uu = 7.005% 2.ud = 5.735% r2dd = 4.696% Year 3 3uuu = 9.199% 3.uud = 7.531% Tudd = 6.166% ryddd 5.048% Spot Rate 1-Year 3.5% 2-Year 4.2147% 3-Year 4.7345% 4-Year 5.2707% Assume that the risk-neutral probability that the annual interest rate moves up or down is 0.5 and par value is $100. 1. Value an option-free bond with four years to maturity using annual spot rates. The annual coupon rate is 6.5% and the coupon is paid annually (once at the end of each year). 2. Value a callable bond with four years to maturity using the binomial interest rate tree. The annual coupon rate is 6.5% and the coupon is paid annually (once at the end of each year). The bond is callable at every coupon payment date. 3. What is the value of the call option embedded in the above callable bond? 4. Value a callable bond with four years to maturity and a two-year call protection period (callable at the end of the second and third years). The coupon rate is 6,5% per period and the coupon is paid once at the end of every period