Fixed Income: Matrix Pricing

Fixed income pricing a Corporate Bond using yield spreads and matrix/interpolation.

You really don’t need the numbers for this, but here it is anyways

If you have a

5 year US T-bond, YTM = 1.48%

5 year A rated Cpt bond, TYM = 2.64%

7 year US T-bond, YTM = 2.15%

7 year A rated Cpt bond, TYM = 3.55%

6 year US T-bond, YTM = 1.74%

and you want to find the required yield on a newly issued 6 year A rated corporate bond.

MY QUESTION: I was wondering why you HAD to use the yield spread method (getting the spread for each the 5 year and 7 year maturity and then interpolating the SPREAD and adding it to the 6 year US t-bond YTM)?

What would be the problem in interpolating the Corporate Bonds directly (ie averaging them out) to get the YTM straight away? For now, I seem to fail to see the flaw in logic of this method.

In this case, the two methods (interpolating the interest rate on the 6-yr corp bond directly directly vs interpolating the spread and then adding it to the 6-year observed treasury yield) give different answers.

the two approaches will give identical answers if and ONLY if the observed yield on the 6-year treasury is equal to the yield on the treasury you’d get by interpolating the 5 and 7-year treasury yields. In this case, the observed 6-year treasury yield of 1.74% is NOT equal to the interpolated treasury yield of 1.815%.

@busprof I don’t know why I just saw this but it seems to make more sense now!

Thanks!!