What are the best methods to extrapolate bond yields from an existing curve that doesn't extend quite this far?

For example, how would one come about finding a theoretical bond yield for a 40 or 50 year US Treasury Bond, when no bond exists of a maturity of much more than 30 years? I guess you could remove credit risk from corporate ultra-long bonds, but this might prove difficult.

I explored using curve fitting models such as Nelson-Siegel and Svensson, but the results are a little unsatisfactory and highly volatile, with theoretical yields at the 50 year mark varying by as more than 50bps depending on the date at which the curve is calculated (over a short time frame).

  • $\begingroup$ Have you got anything out to 50y, like OIS or IRS? Market data for those does exist fairly broadly, but if you don't have them that won't help. $\endgroup$
    – Phil H
    Commented Apr 30, 2013 at 15:57
  • $\begingroup$ I would have recommended Nelson-Siegel...You may get better results if you apply Nelson-Siegel to the forward curve and then build back the yield curve. Alternately, a weighted least squares might help reflect greater uncertainty in the longer bond yields. $\endgroup$
    – John
    Commented Apr 30, 2013 at 17:30
  • $\begingroup$ @PhilH I do have access to some of that data but it appears to be unreliable for the market I'm looking at. That would be an interesting avenue but not quite what I was looking for. $\endgroup$
    – lemarin
    Commented Apr 30, 2013 at 21:08
  • $\begingroup$ @John I will look into using the forward curve instead of the zero curve. I will also look into WLS. Many thanks to both of you. $\endgroup$
    – lemarin
    Commented Apr 30, 2013 at 21:10
  • $\begingroup$ What you guys think about LOESS (local regression) with .99 span to build a less liquid yield curve? $\endgroup$
    – Lisa Ann
    Commented May 2, 2013 at 9:50

1 Answer 1


It really depends on how/where do you plan to use final values. I would not use extrapolation since it will ignore market realities. Forward rates across long end tend to be increasing while dumb extrapolation might give you the opposite result.

In case of treasuries one can use treasury and swap spread and while you do not have 50 Y treasuyy one can find quotes for 50Y swap. You can imply some dynamics of spread or keep it constant and effectively 50Y swap minus spread will be your 50Y treasury yield and than fit curve with that data point. If you have bloomberg check USBE30.

  • 1
    $\begingroup$ Thanks imachbeli, I'll try your method. Obviously it's more art than science. $\endgroup$
    – lemarin
    Commented May 6, 2013 at 14:37

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