3. Construct a 1-year binomial tree with half year of spacing between nodes with the following forward rates calibrated to the market. Node Forward rate Node at time 0 3.0% Node at time 0.5 assuming higher rate 5.0% Node at time 0,5 assuming lower rate 4.0% a. What is the price of a l-year bond with face value $100 and coupon rate of 4%? (5 marks) b. What is the price of a 1-year bond with face value $100 and coupon rate of 6% callable in half year at 100? What is the value of the call option? (10 marks) c. What is the price of a 1-year bond with face value $100 and coupon rate of 2% putable in half year at 100? What is the value of the put option? (10 marks) 3. Construct a 1-year binomial tree with half year of spacing between nodes with the following forward rates calibrated to the market. Node Forward rate Node at time 0 3.0% Node at time 0.5 assuming higher rate 5.0% Node at time 0,5 assuming lower rate 4.0% a. What is the price of a l-year bond with face value $100 and coupon rate of 4%? (5 marks) b. What is the price of a 1-year bond with face value $100 and coupon rate of 6% callable in half year at 100? What is the value of the call option? (10 marks) c. What is the price of a 1-year bond with face value $100 and coupon rate of 2% putable in half year at 100? What is the value of the put option? (10 marks)