I am having a hard time finding books/materials that would teach yield curve pricing using real-world problems/examples

I would like to understand if can I use the below treasury yield data (I believe those are spot rates, also called) to price any treasury bond matching the maturity?

say; I want to price bond maturing in exactly 2 years as of Nov/03/2022,

I take the below zero yields/spot rates,

discount principal+coupon at the 2 year yield, 1st coupon at the 6mon yield, 2nd coupon at the 12 mon yield, and the 3rd coupon at 18 mon yield? all from the picture below.


treasury par yields as of 11/03/2022

1 Answer 1


I'm not sure what books you're using or what I would tell you that's any different, but bonds are priced using discounted cash flow (DCF) models. For a fixed rate bond, if you have discount rates (the Treasury "spot rates" for a government bond), then you just calculate the present value of each cash flow (coupons plus final redemption):

    C1         C2         C3                Cn + P
---------  ---------  ---------  + ... +   ---------
(1+r1)^t1  (1+r2)^t2  (1+r3)^t3            (1+rn)^tn

In your case, you have two coupon periods and the 4th coupon plus par amount (P) with known discount rates, so all you need to do is discount each cash flow to find the fair price of the bond. For the 3rd coupon, you can do a simple linear interpolation or a more complicated interpolation (polynomial, exponential, cubic spline, etc.) to find a rate between the 12 month and 24 month rates. There's not a "right" answer for that, but the difference in price shouldn't be massive just by choosing a different interpolation method.

  • @D Stanley thank you for the reply, I forgot to mention that 18 mon rate is not published, but has to be interpolated. So what I wasn't sure, whether those rates published are spot rates, yield par rayes = spot rate? so say my coupon is 2% I would 102/ 1.0471^4 + 2/1+interpolation^3 + 2/1.0478^2 + 2/1.0457^1
    – Skittles
    Nov 4, 2022 at 14:40
  • Correct - I mention that in my answer. The data you show is the "yield curve" and is what you would use (and interpolate) to find the bond price.
    – D Stanley
    Nov 4, 2022 at 14:52

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