Exercise 1.1 Term Structure Construction

For the Treasury curve with the data given below.

a) Estimate the forward rates assuming they are piecewise

constant.

b) Estimate the forward rates assuming they are piecewise

linear. Ending forward rate for interval equals the starting

forward rate for next interval.

Functional form of the forward rates are given below

Can use excel with the solver function for this exercise.

Tenor Price Coupon Cpn Freq

1 100 0.21% 2

2 100 0.23% 2

3 100 0.28% 2

5 100 0.48% 2

7 100 0.71% 2

10 100 0.97% 2

20 100 1.36% 2

30 100 1.45% 2

Years 0-1 1-2 2-3 3-5 5-7 7-10 10-20 20-30

Constant Beg/End FWD1 FWD2 FWD3 FWD4 FWD5 FWD6 FWD7 FWD8

Years 0-1 1-2 2-3 3-5 5-7 7-10 10-20 20-30

Linear Begin FWD1 FWD1 FWD2 FWD3 FWD4 FWD5 FWD6 FWD7

Linear End FWD1 FWD2 FWD3 FWD4 FWD5 FWD6 FWD7 FWD8

Exercise 1.1 - Term Structure Construction For the Treasury curve with the data given below. Tenor Price Coupon Con Freq 100 0.21% 1 2 2 100 0.23% 2 3 100 2 5 100 2 7 10 100 100 100 0.28% 0.48% 0.71% 0.97% 1.36% 1.45% 2 2 20 30 2 2 100 a) Estimate the forward rates assuming they are piecewise constant. b) Estimate the forward rates assuming they are piecewise linear. Ending forward rate for interval equals the starting forward rate for next interval. Functional form of the forward rates are given below Years Constant Beg/End Years Linear Begin Linear 0-1 FWD1 0-1 FWD1 FWD1 1-2 FWD2 1-2 FWD1 FWD2 2-3 FWD3 2-3 FWD2 FWD3 3-5 FWD4 3-5 FWD3 FWD4 5-7 FWD5 5-7 FWD4 FWD5 7-10 FWD6 7-10 FWD5 FWD6 10-20 FWD7 10-20 FWD6 FWD7 20-30 FWD8 20-30 FWD7 FWD8 End Can use excel with the solver function for this exercise. Exercise 1.1 - Term Structure Construction For the Treasury curve with the data given below. Tenor Price Coupon Con Freq 100 0.21% 1 2 2 100 0.23% 2 3 100 2 5 100 2 7 10 100 100 100 0.28% 0.48% 0.71% 0.97% 1.36% 1.45% 2 2 20 30 2 2 100 a) Estimate the forward rates assuming they are piecewise constant. b) Estimate the forward rates assuming they are piecewise linear. Ending forward rate for interval equals the starting forward rate for next interval. Functional form of the forward rates are given below Years Constant Beg/End Years Linear Begin Linear 0-1 FWD1 0-1 FWD1 FWD1 1-2 FWD2 1-2 FWD1 FWD2 2-3 FWD3 2-3 FWD2 FWD3 3-5 FWD4 3-5 FWD3 FWD4 5-7 FWD5 5-7 FWD4 FWD5 7-10 FWD6 7-10 FWD5 FWD6 10-20 FWD7 10-20 FWD6 FWD7 20-30 FWD8 20-30 FWD7 FWD8 End Can use excel with the solver function for this exercise