Question

1. Consider a 2-year bond with a principal of $100 that provides coupons at the rate of 3.6% per annum semiannually. Suppose the yield on this bond is 5.8% per annum with continuous compounding.
   (a) What is the duration of this bond?
   (b) Suppose the yield on this bond decreases by 0.1%.

   1. Calculate the new bond price exactly.

   2. Estimate the new bond price approximately using duration.

Answer 1

1.
Price=1.8*e^(-5.8%*0.5)+1.8*e^(-5.8%*1)+1.8*e^(-5.8%*1.5)+1.8*e^(-5.8%*2)+100*e^(-5.8%*2)=95.74752

Duration=(0.5*1.8*e^(-5.8%*0.5)+1*1.8*e^(-5.8%*1)+1.5*1.8*e^(-5.8%*1.5)+2*1.8*e^(-5.8%*2)+2*100*e^(-5.8%*2))/(95.74752)
=1.94625

2.
Calculate the new bond price exactly.
=1.8*e^(-5.7%*0.5)+1.8*e^(-5.7%*1)+1.8*e^(-5.7%*1.5)+1.8*e^(-5.7%*2)+100*e^(-5.7%*2)
=95.93405

3.
Estimate the new bond price approximately using duration
=95.74752-95.74752*1.94625/e^(5.8%/2)*(-0.1%)
=95.92854