You work as portfolio risk manager for the defined-benefit pension fund DBPF. The pension fund is invested solely in UK government and corporation bonds. Every morning at 10:00 oclock, you value the bond portfolio using the Nelson-Siegel model for the term structure of interest rates. The Nelson-Siegel model is: () = + [ 1 exp { } ] + exp {/} This model is recalibrated every morning at 9:00 oclock by DBPFs research department. The values of the model parameters this morning are: 0.00024 0.00420 0.00190 1.00000

(a) Amongst the bonds that you have to value are the following three default-free bonds: Bond 1: a zero bond that pays 1000 in 45 days Bond 2: a coupon bond that pays a coupon of 50 in 180 days and the same coupon plus the principal of 1000 in 360 days Bond 3: a zero bond that pays 1000 in 635 days What is the value this morning of each of the three bonds? Explain your calculations carefully.