Question

The six-month zero rate is 3% with continuous compounding. The price of a one-year bond that provides a coupon of 6% per annum semiannually is 99, and the price of a 1.5-year bond that provides a coupon of 8% per annum semiannually is 101.

a. What is the 1.0-year continuously compounded zero rate?

b. What is the 1.5-year continuously compounded zero rate?

Answer 1

1.
3*e^(-3%*0.5)+103*e^(-r)=99
=>r=-ln((99-3*e^(-3%*0.5))/103)
=>r=6.99157%

2.
4*e^(-3%*0.5)+4*e^(-6.99157%)+104*e^(-r*1.5)=101
=>r=-1/1.5*ln((101-4*e^(-3%*0.5)-4*e^(-6.99157%))/104)
=>r=7.21686%