Estimating Discount Factors and Yield Curves from Coupon Bond Prices

Summary

The document sets up a way to infer discount factors from the prices and cash flows of coupon-paying bonds when zero-coupon bonds are unavailable. Each bond price is expressed as the sum of its coupon and principal payments multiplied by discount factors for the relevant payment dates. With several bonds, these pricing equations form a linear system in the unknown discount factors, which can be estimated using linear regression or related methods.

The material is an introductory formulation and asks what the time-series model is called, but it does not specify an estimation procedure, provide a data example, or cite a paper. In practice, identification depends on having enough suitable bonds and sufficiently varied cash-flow schedules; noisy prices, credit or liquidity differences, and constraints on discount factors can also affect estimates. The stated setup groups bonds by comparable characteristics, but it does not explain how to handle irregular payment dates or convert estimated discount factors into a particular yield convention.

Key ideas

• Coupon bond prices can be represented as discounted sums of future coupon and principal payments.
• Each payment date has an associated discount factor that can be treated as an unknown.
• Prices from multiple bonds create a system of equations for estimating discount factors.
• The resulting discount factors can be used to construct a yield curve under a chosen convention.
• The document frames the estimation question but gives no fitted example or specific reference.

Tags

# Yield curve estimaton using linear regression


# 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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.