Problem 1. (60/100) The on-the-run issue for ABC Company is shown below: Maturity 1 2 Yield to maturity Market price 7.50% 7.60% 7.70% 100 100 100 3 Using the bootstrapping methodology, the spot rates are: Maturity Spot rate 1 7.50% 2 7.604% 3 7.71% Assuming an interest rate volatility of 10% for the 1-year rate, the binomial interest rate tree for valuing a bond with maturity of up to three years is shown below: 9.603% 8.481% I 7.50% 7.862% 6.944% 6.437% a) Demonstrate using the 3-year on-the-run issue that the binomial interest rate tree above is in fact an arbitrage free tree. b) Consider a 2-year on-the-run issue, demonstrate that the binomial interest rate tree above is also an arbitrage free tree c) Using the spot rate given above, what is the arbitrage-free value of a 3-year 8.5% coupon issue of ABC Company d) Using the binomial tree, determine the value of an 8.5% 3-year option free- bond e) Suppose that the 3-year 8.5% is callable starting in year 1 at par (100). What is the value of this 3-year 8.5% coupon callable bond? f) What is the value of embedded call option for the 3-year 8.5% callable issue?