# hw10 - A popular model is the Nelson-Siegel family with...

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ORIE 4630 — D. Ruppert Homework #10 — due Friday, Nov 5, 2010 Note: Students are required to work independently on homework. 1. A coupon bond matures in 4 years. Its par is \$1000 and it makes 8 coupon payments of \$21, one every 1/2-year. The continuously-compounded forward rate is r ( t ) = 0 . 022 + 0 . 005 t - 0 . 004 t 2 + 0 . 0003 t 3 . (a) Find the price of the bond. (b) Find the duration of this bond. 2. The maturities ( T ) in years and prices in dollars of zero-coupon bonds are in ﬁle ZeroPrices.txt on Blackboard. The bonds have par = \$1000.
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Unformatted text preview: A popular model is the Nelson-Siegel family with forward rate r ( t ; θ 1 ,θ 2 ,θ 3 ,θ 4 ) = θ 1 + ( θ 2 + θ 3 t )exp(-θ 4 t ) Fit this forward rate to the prices by nonlinear regression using R ’s optim function. (a) What are your estimates of θ 1 , θ 2 , θ 3 , and θ 4 ? (b) Plot the estimated forward rate and estimated yield curve on the same ﬁgure. Include the ﬁgure with your homework. 1...
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