4. (Spot rate project

e) It is November 5 in the year 2011 The bond quotations of Table 4 6 are available. Assume that all bonds make semiannual coupon payments on the 15th of the month. The fractional part of a bond's price is quoted in 1/32nd's Estimate the (continuous- time) term structure in the form of a 4th-order polynomial,

where is time in units of years from today. The discount rate for cash flows at time is accordingly d(r)er Recall that accrued interest must be added to the price quoted to get the total price Estimate the coefficients of the polynomial by minimizing the sum of squared errors between the total price and the price predicted by the estimated term structure curve Plot the curve and give the five polynomial coefficients

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TABLE 4.6 Bond Quotes Coupon Maturity Ask price 6 6 9 Feb-2012 100:0 Feb-2012 100:22 7 00 0000 Aug-2012 100:24 Aug-2012 101:1 Feb-2013 101:7 7 Feb-2015 Feb-2013 101:12 00 8 Aug-2013 100:26 00000000 F 8 Aug-2013 102:1 Feb-2014 98:5 Feb-2014 102:9 Aug-2014 97:13 Aug-2014 101:23 99:5 Feb-2015 109:4 8 Aug-2015 101:13 10% Aug-2015 107:27 7/1 Feb-2016 99:13 8 Feb-2016 103:0