Question

The current price of a 6-month zero coupon bond with a face value of $100 is B1. If a 9-month strip with a face value of $100 is currently trading for B2, find the forward interest rate for the 6 to 9 month period. Solve by both continuous compounding and quarterly compounding. Write your answers for the following:

10. Six-month spot interest rate for quarterly compounding.

11. Nine-month spot interest rate for quarterly compounding.

12. Forward rate (6 to 9 months) for quarterly compounding.

13. Six-month spot interest rate for continuous compounding.

14. Nine-month spot interest rate for continuous compounding.

15. Forward rate (6 to 9 months) for continuous compounding.

16. What is the guaranteed fair price of a 3-month T-Bill to be delivered at 6 months from now, assuming quarterly compounding?

17. What is the guaranteed fair price of a 3-month T-Bill to be delivered at 6 months from now, assume continuous compounding?

B1 = 97.65

B2 = 96.65

CAN YOU PLEASE SHOW WORK

Answer 1

PART 10.

Six-month spot interest rate = {(100 / Current Price of Zero-Coupon Bond)^1/2 - 1} x 4

= {(100 / 97.65)^1/2 - 1)} x 4

= (1.01196123452 - 1) x 4

= 0.04784

= 4.784% compounded quarterly

PART 11.

Nine-month spot interest rate = {(100 / Current Price of Strip)^1/3 - 1} x 4

= {(100 / 96.65)^1/3 - 1)} x 4

= (1.01142274 - 1) x 4

= 0.04569

= 4.569% compounded quarterly

PART 12.

Forward rate (6 to 9 months) = {[(100/Current Price of Strip) / (100/Current Price of Zero Coupon Bond)] - 1} x 4

= [{(100/96.65) / (100/97.65)] - 1} x 4

= {(1.03466114847 / 1.02406554019) - 1} x 4

= 0.04139

= 4.139% compounded quarterly

PART 13.

Six-month spot interest rate for continuous compounding

= log_e(Six-month spot rate)

= log_e(100/97.65)

= log_e(1.02406554019)

= 0.023780528661

= 2.378% compounded continuously

- The log value is calculated through online calculator.

- Only four sub-parts are allowed to be answered.