# Yield curve estimaton using linear regression

Assuming that there are not any zero coupon bonds in the market, then someone has to use the prices of regular bonds with same maturity and characteristics (risk,issue etc.) to obtain the yield curve. One method, as the lectures notes mention, is to use linear regression for different bonds: $P_{A,0}= \frac{C_1}{(1+r)} + \frac{C_2}{(1+r)^2}+...+ \frac{C_n + P}{(1+r)^n}$

Set: $d_1= \frac{1}{1+r} ,..., d_n=\frac{1}{(1+r)^n}$

Then: $P_{A,0}= C_1 d_1 +C_2 d_2 ... +(C_n +P_n)d_n$

We have in our example 4 different bond ( A,B,C and D) $P_{A,0}= C_{A1} d_{A1} +C_{A2} d_{A2} ... +(C_{An} +P_{An})d_{An}$

$P_{B,0}= C_{B1} d_{B1} +C_{B2} d_{B2} ... +(C_{Bn} +P_{Bn})d_{Bn}$

$P_{C,0}= C_{C1} d_{C1} +C_{C2} d_{C2} ... +(C_{Cn} +P_{Cn})d_{Cn}$

$P_{D,0}= C_{D1} d_{D1} +C_{D2} d_{D2} ... +(C_{Dn} +P_{Dn})d_{Dn}$

How is this time-series model called? A paper with reference to this is welcomed.

• If you have 4 bonds with same characteristics except for price and coupon you are attempting to find a rate, r, which minimises the least squares regression. Not sure what your question is in relation to time-series? – Attack68 Mar 12 '18 at 15:38
• The coupons are in different periods. I tried estimating and OLS regression but assuming that coupon rate is fixed, the model produces collinearity ($C_{A,i}$ is the same for $i=1,2,..,n$) – alexbougias Mar 12 '18 at 17:18
• for different risky issuers, $d_{A1}$, $d_{B1}$, $d_{C1}$, and $d_{D1}$ are not quite comparable, so you can't use one variable to represent all; for the same issuer or all risk-less issuers in theory, it's not quite meaningful because bonds of the same maturity should have the same yield. – Will Gu Apr 19 '18 at 19:12