[n this assignment you will estimate the term structure model proposed by Nelson and Siegel (1987'). In the model, on any given date the instantaneous forward rate that applies at maturity 1' is =a+ark+a0 where flu, ,8], 132 and A are model parameters. The zero rate that applies to maturity r is then given by 1 e'A" AT d=a++a )are Questions 1. The U.S. Department of the Treasury publishes every day the Daily Treasury Par Yield Curve Rates. With your own words, briey explain what is the Treasury par yield curve, and how market practitioners could use this information. 2. The daily Treasury par yield curve rates are reported for 1, 2, 3 and 6 months, and for 1, 2, 3, 5, 7, 10, 20 and 30 years. Using all these maturities, estimate the Nelson-Siege] model on the following dates: . 3f15f2007 . 3f16f2009 . 3f16f2015 . 12f14f201s . 3g23/2020 . 2f2f2022 Follow the procedure that I used in class, that is, minimise the sum of the square pricing errors N S = 2(a- ember. i=1 where P and PM\": denote the true and model implied price of each bond, respectively, and N is the number of bonds used on a given day in your estimation. Of course, do not use the the 2-month rate if it is not available. In a nicely formatted table, for each date report your estimates for ,80, ,81, g and A. Also report the root-mean square error dened as RMSE = 1/5\" {N . 3. For each date mentioned in the previous point: II Generate a plot that shows the daily term structure of zero rates for maturities ranging from 0 to 30 years. a Describe the shape of each the term structure of zero rates, and relate your description to the macro-economic environment prevalent on those dates. 4. Using the parameters computed on 2/2f2022, compute the invoice and flat price of a Treasury bond paying semiannual coupons of 1.875% per year over a notional of $100 with maturity date 11/15/2051. Also report the yield-tomaturity of the bond expressed as a rate per year with semi-annual compounding. 5. Redo 2. by restricting ,6: = 0. Briey comment on the advantages (if any) of the Nelson- Siegel model over the restricted model