Questions 13 a. An investor buys a five year cap on 3-mth LIBOR at 3% on a notional amount of 10m. She also buys a five year floor on 3-mth LIBOR at the same strike (3%) and on the same notional amount (10m). Set out her future cash flow and discuss the beliefs about future interest rates that may have led her to put on such a trade. [5%] b. What is the relationship between the price of a cap, the price of a floor and the value of a swap with the same maturities, reset dates, strike prices and notional? Justify your answer. C. [5%] Consider the following binomial model of the 1-year interest rate where the rate goes up or down by 1% each year with a (risk-adjusted) probability of an up-move is 50%: 6% 5% 4% 4% 3% 2% Compute the 1, 2 and 3 year spot rates. [5%] d. Current 1, 2 and 3 year spot rates are 1.00%, 1.50% and 2.00%. Explain the method by which you could adjust the model in part (c) above to fit the current term structure. Give a rough estimate of what the numbers in the adjusted tree would be. [5%] Questions 13 a. An investor buys a five year cap on 3-mth LIBOR at 3% on a notional amount of 10m. She also buys a five year floor on 3-mth LIBOR at the same strike (3%) and on the same notional amount (10m). Set out her future cash flow and discuss the beliefs about future interest rates that may have led her to put on such a trade. [5%] b. What is the relationship between the price of a cap, the price of a floor and the value of a swap with the same maturities, reset dates, strike prices and notional? Justify your answer. C. [5%] Consider the following binomial model of the 1-year interest rate where the rate goes up or down by 1% each year with a (risk-adjusted) probability of an up-move is 50%: 6% 5% 4% 4% 3% 2% Compute the 1, 2 and 3 year spot rates. [5%] d. Current 1, 2 and 3 year spot rates are 1.00%, 1.50% and 2.00%. Explain the method by which you could adjust the model in part (c) above to fit the current term structure. Give a rough estimate of what the numbers in the adjusted tree would be. [5%]