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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

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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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  • $\begingroup$ let me make sure i understand. So you are saying recreate a yield curve for each time period t going back to t-n. Then once I have that series, I can create a theoretical profit/loss on the bonds over time? $\endgroup$
    – user2179795
    May 9, 2018 at 21:00
  • $\begingroup$ To do this you need data on multiple bonds across a spectrum of maturities for each time period t. In each period construct a bond curve as the LSE estimator discount curve of those bonds, using some interpolation scheme. That curve gives a means of valuing any respective bond at time period t. Repeat for all time periods. Now from each bond curve at each time period calculate those prices (or YTMs) you care about. This is a consistent mechanism and to stay true to it you should also it for the time periods you have the real data for your bond, even when that model system differs slightly $\endgroup$
    – Attack68 ♦
    May 9, 2018 at 21:09
  • $\begingroup$ Very interesting. How do you choose the spectrum of maturities at a given time? $\endgroup$
    – AK88
    May 10, 2018 at 3:54
  • $\begingroup$ @AK88 the spectrum is often by default. Many countries or credits do not have sufficient bonds to chooses from effectively so you are forced to use what you have. Very liquid markets such as US treasuries and other major gov bonds markets allow you to be selective but there are probably nuanced reason in each currency why you might choose to include some and exclude some. For example in Europe the 'CAC (collective action clause)' is a feature of some but not all bonds! $\endgroup$
    – Attack68 ♦
    May 13, 2018 at 6:48
  • $\begingroup$ Is it safe to proceed with key rate maturities then? $\endgroup$
    – AK88
    May 13, 2018 at 7:00

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