Question

Assume that discount factors are as given below. Compute the par rates out to two years at semiannual intervals.

T (in years)	Z(T)
0.50	0.9768
1.00	0.9518
1.50	0.9252
2.00	0.8976

Hint: Use the formula from class for the par yield C(T).

Note! The formula gives you a decimal number, i.e. a number like 0.031875. This number means 3.1875%.

1) Calculate the 6-month par yield . Write your answer as a decimal with six digits after the decimal point (e.g. 3.1875% is to be entered as 0.031875)

2) Calculate the 1-year par yield . Write your answer as a decimal with six digits after the decimal point (e.g. 3.1875% is to be entered as 0.031875)

3) Calculate the 1.5-year par yield . Write your answer as a decimal with six digits after the decimal point (e.g. 3.1875% is to be entered as 0.031875)

4) Calculate the 2-year par yield . Write your answer as a decimal with six digits after the decimal point (e.g. 3.1875% is to be entered as 0.031875)

Answer 1

SOLUTION:-

1) C(0.5) = 2*(1-Z(0.5))/(Z(0.5))

C(0.5) = 2*(1-0.9768)/0.9768

C(0.5) = 0.047502

2) C(1) = 2*(1-Z(1))/(Z(0.5) + Z(1))

C(1) = 2*(1-0.9518)/(0.9768 + 0.9518)

   C(1) = 0.049984

3) C(1.5) = 2*(1-Z(1.5))/(Z(0.5) + Z(1) + Z(1.5))

C(1.5) = 2*(1-0.9252)/(0.9768 + 0.9518 + 0.9252)

   C(1.5) = 0.052421

4) C(2) = 2*(1-Z(2))/(Z(0.5) + Z(1) + Z(1.5) + Z(2))

C(2) = 2*(1-0.8976)/(0.9768 + 0.9518 + 0.9252 + 0.8976)

   C(2) = 0.054593

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