Suppose the current one-year swap rate y_0[0, 1] is 1.47%, and the two-year and three-year swap rates. y_0[0, 2] and y_0[0, 3], are 2.05% and 2.38%, respectively. They are quoted with annual payments (so alpha = 1). Calculate Z(0, 1), Z(0, 2), Z(0, 3), and P_0[0, 3]. Remember P_0[0, 3] is the present value of a three-year annuity paying 1 per year. The process of calculating ZCB prices from swap rates is called bootstrapping. Because swaps are so widely traded and so liquid, swap rates are typically the "primitive" source of information from which ZCB prices, labor, and other interest rates are calculated. Recall that the annually compounded zero rate for maturity T is the rate r such that Z(0, T) = (1 + r)^-T. Calculate the one-year, two-year, and three-year annually compounded zero rates. The graph of y_0[0, T] versus T is called a yield curve. Suppose the yield curve is upward sloping, in other words, y_0[0, T_1] > y_0[0, T_2] whenever T_1 > T_2. Will the zero rates be higher or lower than swap rates? An approximation sometimes used to calculate the present value of, for example, a three-year annuity is to discount each payment at the the three-year swap rate. In other words, the approximation Z(0, n) = (1 + y_0[0, 3])^-n for n = 1, 2, 3 is used. This approximation is called internal rate of return (IRR) discounting. Calculate the error in valuing the annuity from (a) with IRR discounting. Use the ZCB prices calculated in (a) to calculate the current price of a three-year fixed rate bond of notional 1 and annual coupons of c = y0 [0, 3] = 2.38%. Use IRR discounting with rate y_0[0. 3] = 2.38% to calculate the price of the bond in (e). How does it compare to the price calculated in (e)