Reconstructing Historical Bond Yields with a Smooth Curve
Summary
The document considers how to extend a bond’s historical yield or price series beyond the period when that individual bond existed. Its proposed approach is to fit a smooth curve to a group of comparable bonds at each point in time, choosing the curve to reprice the observed bonds with a least squares objective. Once fitted, the curve can provide an estimated yield or price for a target maturity even when no single bond spans the full history.
The answer illustrates the idea with a bond whose maturity changes in tenor as the observation date moves backward, and explains that the fitted curve represents the market’s maturity structure at each date. It cautions that bonds have individual richness or cheapness, so concatenating their raw time series can introduce distortions. The source offers a conceptual recommendation, not a specification of curve model, bond selection rules, liquidity adjustments, or empirical comparison; resulting estimates inherit fitting error and curve assumptions.
Key ideas
- Fit a maturity curve to comparable bonds separately at each observation date.
- Use the fitted curve to estimate a yield or price at maturities not represented by one continuous bond series.
- A least squares objective can balance repricing observed bonds against keeping the curve reasonably smooth.
- Raw bond series can differ because individual securities may trade rich or cheap.
- Curve estimates depend on model choices and retain fitting error.
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Full text
# Recreating / Extending Bond Time Series # Recreating / Extending Bond Time Series I am trying to analyse historical yield curve dynamics within an across countries and step one is extending / recreating historical yields and/or prices. The challenge is this: lets say a 10 year bond is issued in 2008 is due 2018. I will only have price / rate data for that time frame, but I need to extend this timeseries to look back across a wider time frame. How have you thought about this problem? Has anyone combined times series of multiple bonds? What was your approach? Thanks ## Answer by Attack68 (score 1) https://quant.stackexchange.com/a/39709 The most natural thing to do when considering this kind of generic maturity analysis of bonds is to use a similar series of bonds to derive a bond curve which represents a single yield curve that reprices them minimising the least squares error (you want a reasonably smooth curve that doesn't necessarily price them all precisely but captures the generalist structure). This way you build a system whereby you can derive any price you want for any maturity at any time (within the error imposed by your system). Let's say you went back to 1998 and priced a bond with maturity of 2018, in that instance the bond would represent a 20Y and your constructed curve in that sector would reflect prices of the 20Y bonds at that time. Note that you can't directly combine time series of different bonds because each bond has inherent characteristics that make it slightly cheaper or slightly more expensive and therefore when you merged the timeseries you have to account for that difference, which would no doubt introduce more error that the method above and be far more subjective and arbitrary for research purposes.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.