Fitting the Yield Curve Suppose you work as a quant for the FICC desk at one bank, and you are responsible for updating the in-house yield curve of US Treasuries. Specifically, you have the data from the following bonds. The bonds all have annual coupon payments and notion $100 per bond. (a) Using the relation of absence of arbitrage, derive the prices of 1-year to 5-year zero coupon bonds with notion $1. (b) Using the prices obtained in (a), derive the continuously-compounded yields of the zero coupon bonds. (c) Fit the a Nelson-Siegel model yield curve to the yields you computed. You can set the scale parameter =3, and obtain the factors determining the curve using regression: y1y2y5=1111(1e1/)2(1e2/)5(1e5/)1(1e1/)e1/2(1e2/)e2/5(1e5/)e5/012+. In the same figure, plot the yields you computed in (b) and the fitted yield curve in (c). (d) Based on the observation, can you form a trading such that the portfolio is immune to movement in level and slope? You should involve only 3-, 4- and 5-year bonds as mentioned in your portfolio. Report the relevant weights and your portfolio's exposure to curvature of the yield curve. (e) Technically, what are you betting for the portfolio in (d)