Assume that the continuously-compounded spot yield curve is as follows: r(0,0.5) = 1.2%, r(0,1) = 1.6%, r(0,1.5) = 2%, r(0,2) = 2.2%. . a) Calculate the price of a 0.5-year, a 1-year, a 1.5-year, and a 2-year zero-coupon bond. Moreover, calculate the swap rate of a two-year swap with semi-annual payments. b) Assume that the drift parameters 0; in a Ho-Lee model are equal to 0.01 for i = 0,1,2, and the volatility parameter o is equal to 1.5%. Build a three-step interest-rate tree with A = 0.5. Use this Ho-Lee model to calculate the model-implied price of a 0.5-year, a 1-year, a 1.5-year, and a 2-year zero-coupon bond. Do these prices agree with the observed spot yield curve? c) Fit the drift parameters 0; (i = 0,1,2) in the previous Ho-Lee model so that the model matches the observed spot yield curve perfectly. What are the @ values? d) Use the fitted Ho-Lee tree to calculate the price of a two-year, at-the-money cap with semi- annual payments, and a notional of $100. Moreover, calculate the price of a two-year, at- the-money floor with semi-annual payments, and a notional of $100. Comment on the relationship between the cap and floor price. (Note: the strike rate of an at-the-money cap/floor is equal to the swap rate.) Assume that the continuously-compounded spot yield curve is as follows: r(0,0.5) = 1.2%, r(0,1) = 1.6%, r(0,1.5) = 2%, r(0,2) = 2.2%. . a) Calculate the price of a 0.5-year, a 1-year, a 1.5-year, and a 2-year zero-coupon bond. Moreover, calculate the swap rate of a two-year swap with semi-annual payments. b) Assume that the drift parameters 0; in a Ho-Lee model are equal to 0.01 for i = 0,1,2, and the volatility parameter o is equal to 1.5%. Build a three-step interest-rate tree with A = 0.5. Use this Ho-Lee model to calculate the model-implied price of a 0.5-year, a 1-year, a 1.5-year, and a 2-year zero-coupon bond. Do these prices agree with the observed spot yield curve? c) Fit the drift parameters 0; (i = 0,1,2) in the previous Ho-Lee model so that the model matches the observed spot yield curve perfectly. What are the @ values? d) Use the fitted Ho-Lee tree to calculate the price of a two-year, at-the-money cap with semi- annual payments, and a notional of $100. Moreover, calculate the price of a two-year, at- the-money floor with semi-annual payments, and a notional of $100. Comment on the relationship between the cap and floor price. (Note: the strike rate of an at-the-money cap/floor is equal to the swap rate.)