Matrix Pricing of bonds

CFA Level I
#1

Hi,

Can anyone explain matrix pricing of bonds with an example? I am having a tough time understanding it on my own.

#2

Hello,

Consider the following:

  • 5 year, 5% annual pay coupon bond with YTM= ???

Comparing this bond with the following bonds:

  • 6 year, 5% annual pay coupon bond, with YTM= 6%
  • 4 year, 5% annual pay coupon bond, with YTM= 5.5%

This is how it will look like:

l_________________l__________________l

4 year 5 year 6 year

5.5% 6%

Using linear interpolation,

YTM (of the bond in question)= 5.5% + [(5-4)/(6-4) * (6%-5.5%)]= 5.75%

Since 5 year is the mid point of 4 year and 6 year, an alternative method will be to take the simple average of the two YTM (i.e. 5.5% and 6%).

Hope it helps a bit.

Cheers,

Ernest

#3

Matrix prices are quoted prices for securities with same maturities and ratings rather than a fix price for desigmated security . Matrix means interpolating in the matrix format.They are used under highly liquid positions.

#4

Thanks guys …

#5

Why linear interpolation is used??

#6

Because it’s easy.

#7

I mean why we’re not using the average?

#8

Linear interpolation _ is _ an average: a weighted average.

If you know the price of a 1-year bond and the price of a 5-year bond, but not the prices of any bonds with maturities between 1 year and 5 years, would you use the same (unweighted average) price for a 2-year bond, a 3-year bond, and a 4-year bond?

#9

Got it. Thank you.

#10

You’re quite welcome.

#11

is there any hard and fast formulae for linear interpolation?

#12

What do you mean ? Linear interpolation is unitary method. What could be harder than that ?

#13

Yes.