Assessing Exponential Spline Coefficient Stability in Treasury Models

Summary

The document asks whether the beta coefficients in an exponential-spline discount-function model remain stable from day to day. The motivation is practical: if the coefficients move predictably with benchmark bond prices, a researcher might use the model’s price sensitivities to estimate coefficient changes and update prices for other bonds in real time.

The reply points to historical US Treasury beta estimates extending back to 1992 and notes that stability depends on the observer’s threshold. The text provides no details about the plotted estimates, estimation procedure, or measured variation, so it does not establish whether the coefficients are stable enough for real-time pricing. The proposed sensitivity-based approximation is an idea raised by the questioner, not a method tested or validated in the document.

Key ideas

• The model represents the discount function as a sum of exponentially decaying terms weighted by beta coefficients.
• The question is whether beta estimates are stable enough to support real-time bond price approximation.
• Price sensitivities could be used to relate benchmark price changes to estimated coefficient changes.
• Historical US Treasury beta estimates are cited, but the document gives no quantitative stability results.

Tags

# How stable are the coefficients in the Exponential Spline model?


# How stable are the coefficients in the Exponential Spline model?












In the model defined below for discount function, are the Beta's relative stable from day to day? If so I might use Hessian dPdB to invert the Beta changes from benchmark price changes, and then to approximate all the other bond model prices in real time. Haven't tried yet, but my intuition is Beta's won't be stable so the approx won't work. thanks in advance if anyone tried this before.

$$ df(t)=\sum_{n=1}^N \beta_n \exp(−n⋅\alpha⋅t). $$

## Answer by Helin (score 2)

https://quant.stackexchange.com/a/65679

I think different researchers might have different thresholds for what they perceive to be "stable." FWIW, the picture below provides our beta estimates going back to 1992 for the US Treasury market:

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.