Question

The continuously compounded six-month zero rate is 6.50% per annum. The price of a one-year bond that provides a coupon of 7.00% per annum semiannually is 93.50. What is the one-year continuously compounded zero rates? Please put answer within two decimol places.

Answer 1

Given that,

six-month zero rate r0.5 = 6.5% compounded continuously

price of a one year 7% semiannual coupon bond is $93.50

face value = $100

semiannual coupon payment = (7%/2) of 100 = $3.5

let one year continuously compounded zero rate be r1

So, price of the bond is calculated using formula

Price = C*e^(-r0.5*0.5) + (C+FV)*e^(-r1)

=> 93.50 = 3.5*e^(-0.065*0.5) + 103.5*e^(-r1)

=> e^(-r1) = 0.8706

=> r1 = 13.85%

So, one-year continuously compounded zero rates is 13.85%