# How can I compute zero coupon bond prices from dirty/clean prices of coupon bonds?

I am having problems with computing zero-coupon bond prices. The question is the following:

Today is $t$=14.4.2016 and I know dirty and clean prices of coupon bonds expiring at maturities: 4.7.2016, 4.7.2017, 4.7.2018,4.7.2019, 4.7.2020,4.7.2021. Coupons are paid annually on the date of maturity.

How can we determine the term structure of zero-coupon bond prices?

My idea is simply to apply the formula:

$P_{dirty}(t) = \sum_i^n c_i P(t,T_i)$

Starting from the bond A expiring on the 4th July 2016, we should have

$P_{dirty}^A (t)=c^A P(t,4.7.2016)$

from which we can compute the first discount factor. Then, considering the other bonds, recursively, we should be able to compute them all.

Finally, employing these results and the method of least squares (assuming a parametric form of the term structure) we should be able to estimate the term structure.

The issue is that the discount factors $P(t,T_i)$ turn out to be bigger than $1$, which impossible. Can you help me?

Is the formula above correct?

I can provide you with all the numerical values, if you need them.

• What is $c_i$? Make sure that $c_i$ is equal to the i-th coupon, except for the last one $c_i,i=n$ which equals 100+coupon. – Alex C May 1 '16 at 13:50
• Yes, sure! $c_i$ is exactly what you said :) – Fred G. May 1 '16 at 15:45
• Anyway, did I use the dirty price correctly? What if I considered $P_{clean}(t)=\sum_i c_i P(t,T_i)$? – Fred G. May 1 '16 at 15:48