Par yield from theoretical continuous compounded spot rates?

[Dingwen]

Hi all.

Hull chapter 4 notes Q2: What is the two-year par yield with continuous compounding given the theoretical continuous compounded spot rates (2.0% 0.5 years, 3.0% 1.0 years, 4.0% 1.5 years, 5.0% 2.0 years)?

Answer provided stated that "5.0% semi-annual coupon rate is the solution that prices the bond exactly at par given this theoretical spot rate curve". Then they converted the discrete rate into continuous rate of 4.94%.

How did they conclude that it's a 5.0% semi-annual coupon?

 

[ShaktiRathore]

Hi
First calculate coupon which shall yield 5% value of coupon as 5% or .05*100=5 from the equation
c/2*exp(-.5*.02)+c/2*exp(-.03*1)+c/2*exp(-.04*1.5)+c/2*exp(-.05*2)+100*exp(-.05*2)=100
The answer states coupon yield that would value bond at par using given spot rate curve. Solve for c it should yield 5% semi coupon value. Also coupon yield is also par yield as bond is prices at par.we obtained par yield as discrete as coupon yield is always discrete therefore we need to convert 5% to continous to get continous par yield as 2*ln(1+.05/2)=4.94%
Thanks