I need to obtain the initial parameters that would be used in the Non-Linear Optimization that provides the Nelson-Siegel Svensson parameters for US Treasury Bonds. The Optimization appears to be very sensitive to input parameters and so the initial Ordinary Least Squares Regression that I do to get them is of critical importance. My code is such that if I pass the actual yields to the OLS regression I get the same parameters in that link, which mean the code works and my selection process for the bonds that go into the code is wrong.

My selection method for the bonds: 3 month, 6 month, 9 month, 2 year, 3 year, 5 year, 10 year and 30 year on-the-run par treasury bonds.

I have tried multiple different sets of bonds, but none of them have resulted in initial parameters close to those in the second link, which should be the case.

And one further question I have is, if I do end up obtaining a selection method that provides appropriate parameters, could I apply this to Bonds issued by other Governments? Is there a general selection procedure that tends to work across various currencies?

Please let me know if I need to provide more information.

Thank You


1 Answer 1


There could be many reasons:

  1. You're using on-the-run yields, but the Fed's fitted curves are off-the-run yield curves.
  2. You're using only a few points on the curve, the Fed uses virtually all outstanding issues.
  3. The optimization, as you stated, is unstable. There's also no guarantee that the Fed's parameters are necessarily the best. If you look at the historical time series of the parameters, they're in fact very noisy and jumpy.
  • $\begingroup$ Thank You. I tried incorporating 1. and 2. of your answer and obtained initial parameters of [7.086969157340016, -7.945088603826978, -18.673404065407503, 35.094818521466046, 1.5800000000000103, 0.6000000000000341] from the OLS Regression, which seem to be very far off of the actual parameters on the Fed Site. I know you said there could be many reasons for this, but are there any that spring to mind? $\endgroup$
    – Jojo
    Aug 10, 2015 at 20:49
  • 1
    $\begingroup$ Can you explain how you addressed 1 & 2? What source did you use for prices? What's the pricing time of your bonds? (3pm, 4:30pm, 5pm?) There are too many factors. Unless the resulting yield curves are wildly different, I wouldn't worry too much about it. $\endgroup$
    – Helin
    Aug 10, 2015 at 21:29

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