A range bond is a structured security, which can be described as follows: It is like a standard coupon bond, but it pays the coupon at some given Period i if the reference interest rate in Period i-1 is within a given interval; otherwise, it pays no coupon in that period. In any case, it will pay the principal at maturity T. Consider a 1-year range bond at Time i=0, with an annual coupon rate equal to 5%. The range bond pays semi-annually the coupon in Period i if the continuously compounded 6-month interest rate in Period i-1 is within the interval [0.025,0.05]. Given the above 2-step binomial tree of interest rates, and the yield curve (of continuously compounded interest rates) at t=0 as below Maturity Yield 0.5 2.7% 1 2.96% 1.5 3.34% 2 3.81% answer the following questions: a. Given that ri.j either increases rij + mA + ov or decreases to rij + m 4 - ov in the next period, where A is the passage of time in years between two periods, calculate the o implied by the above interest rate tree and explain what o means in fixed income securities. b. Following Question B-1, calculate 13.dud if we extend the above binomial tree of interest rates to 3 steps and m2 = 0.4. c. What is the risk-neutral probability in period i=0? d. What is the risk-neutral probability in period i=1? e. What are the possible cash flows of the range bond at maturity? f. What is the price of the range bond? What is the spot rate duration of the range bond in Period 0? h. Using the short-term bond that matures in the next period and the long-term bond that matures in period i=3, describe the dynamic replication strategy of the range bond. A range bond is a structured security, which can be described as follows: It is like a standard coupon bond, but it pays the coupon at some given Period i if the reference interest rate in Period i-1 is within a given interval; otherwise, it pays no coupon in that period. In any case, it will pay the principal at maturity T. Consider a 1-year range bond at Time i=0, with an annual coupon rate equal to 5%. The range bond pays semi-annually the coupon in Period i if the continuously compounded 6-month interest rate in Period i-1 is within the interval [0.025,0.05]. Given the above 2-step binomial tree of interest rates, and the yield curve (of continuously compounded interest rates) at t=0 as below Maturity Yield 0.5 2.7% 1 2.96% 1.5 3.34% 2 3.81% answer the following questions: a. Given that ri.j either increases rij + mA + ov or decreases to rij + m 4 - ov in the next period, where A is the passage of time in years between two periods, calculate the o implied by the above interest rate tree and explain what o means in fixed income securities. b. Following Question B-1, calculate 13.dud if we extend the above binomial tree of interest rates to 3 steps and m2 = 0.4. c. What is the risk-neutral probability in period i=0? d. What is the risk-neutral probability in period i=1? e. What are the possible cash flows of the range bond at maturity? f. What is the price of the range bond? What is the spot rate duration of the range bond in Period 0? h. Using the short-term bond that matures in the next period and the long-term bond that matures in period i=3, describe the dynamic replication strategy of the range bond