Bond Pricing

[Anne]

Hi I'm new to these boards

I know in any online community its never good for a first post to be something like this, but it looks like there's lots of members here so I'm going to give it a shot.

I want to know how I go about pricing a coupon bond given the price of another coupon bond (the two have the same 10 year maturity).

I've also been given the forward rate between year 5 and 10 and the 5 year spot rate.

Would be great if I can get some pointers here.

 

[Tsotne]

You have 2 alternatives: Either purchase the 10 years bond or break it into 5 years bonds 2 times. Put another way, buy the 5 years bond and after the maturity date buy another 5 years bond. So the pricing requires you to adjust simply the coupon interest with regard to forward rate. Converting the forward rate to coupon rate is straightforward.

 

[pathfinder]

You can find out the bond price using bootstrapping

Let X be the bond price of second Bond and C be the cupon and P the face value of the Bond.

Five year forward rate be f5 and spot rate be r5
10 year discount factor is D = ( 1 / ( (1+f5)^5)* ((1+r5)^5) )

X = C( 1/Y1 + 1/Y2^2 .... + 1/ Y9^9 + 1/Y10 ^10 ) + P *D


Where Y1 .. Y10 are the discount rates from the yield cure

let d =(1/Y1 + 1/Y2^2 .... + 1/ Y9^9 + 1/Y10 ^10)

X=Cd +PD

slove for d

d= (X-PD)/C
==================================
Let X be the bond price of the bond that you want to find . C the cupon and P the face value of the Bond.

the Bond price will be
X= Cd +PD

 

[vincegata]

Nelson - Siegel bootstrapping.