The maturities (T) in years and prices in dollars of zero-coupon bonds are in ¯le ZeroPrices.txt on the book's website. The prices are expressed as percentages of par. A popular model is the Nelson{Siegel family with forward rate
r(T; θ1; θ 2; θ 3; µ4) = µ1 + (µ2 + µ3T) exp(¡µ4T):
Fit this forward rate to the prices by nonlinear regression using R's optim function.
(a) What are your estimates of θ1; θ2; θ3; and θ4?
(b) Plot the estimated forward rate and estimated yield curve on the same ¯gure. Include the ¯gure with your work.