Why Treasury Curve Fits Depend on Bond Selection and Optimization
Summary
The document examines why an ordinary least squares initialization for fitting a Nelson–Siegel–Svensson yield curve may not reproduce a reference set of parameters. The questioner uses selected on-the-run US Treasury maturities to estimate starting values for a later nonlinear optimization and asks whether the approach can generalize to other governments’ bonds.
The response identifies several sources of mismatch: the reference Federal Reserve curve uses off-the-run yields rather than on-the-run issues, and it draws on nearly all outstanding securities rather than a small set of maturities. It also cautions that the nonlinear optimization can be unstable and that published fitted parameters are not necessarily uniquely best; their historical series can be noisy. The document offers no general bond-selection recipe and does not establish a cross-country procedure. Its practical lesson is that the security universe and fitting method must match the reference curve before parameter differences can be diagnosed as a coding problem.
Key ideas
- A fitted yield curve can differ from a reference curve because the underlying bond universe differs.
- The Federal Reserve fit discussed in the answer uses off-the-run securities and a much broader set of issues.
- Nonlinear Nelson–Siegel–Svensson optimization can be sensitive to its starting parameters.
- Fitted curve parameters may be noisy and need not represent a uniquely best solution.
- The document does not provide a universal bond-selection method for different governments.
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Full text
# Selecting bonds to be used in Nigel-Siegel Svensson OLS Regression # Selecting bonds to be used in Nigel-Siegel Svensson OLS Regression 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 ## Answer by Helin (score 1, accepted) https://quant.stackexchange.com/a/19256 There could be many reasons: - You're using on-the-run yields, but the Fed's fitted curves are off-the-run yield curves. - You're using only a few points on the curve, the Fed uses virtually all outstanding issues. - 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.
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