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Model for Pricing Zero-Coupon Treasury Bonds

Posted 11 years ago
I have developed a model for fitting zero-coupon Treasury bonds to price data.  It can take data from a Wall Street Journal public page or data from a brokerage account web page may be pasted into the Mathematica notebook and analyzed.  Here is an example of a recent fit.

The blue dots are data points and the red line the fit.  Below are the parameter statistics.

The model is based on the survival function of a probability distribution which is the sum of an exponential distribution random variable and a gamma distribution random variable.  The formula is obtained as follows:
(*I haven't been able to do this with Integrate[].**)
(*For fitting the price model the constraint r0 != r1 has to be added**)
td = TransformedDistribution[
   x + y, {x \[Distributed] ExponentialDistribution[r0],
    y \[Distributed] GammaDistribution[k, 1/r1]}];
SurvivalFunction[td, t] // FullSimplify

The model is then fit with NonlinearModelFit[] using some initial parameter starting points.  The model is described in detail at the website below.

Or the Mathematica notebook containing all the functions can be opened with the following line of code:
Why this should work so well is something of a mystery.  Is it another case of "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," or does it point to some underlying truth?  Comments and ideas will be appreciated
POSTED BY: Robert Rimmer
3 Replies
Posted 11 years ago
I have updated the original topic with a better model containing only three parameters.  The associated Mathematica notebook has also been updated.  The model has some interesting mathematics, which I doubt would have ever been discovered without Mathematica.
POSTED BY: Robert Rimmer
Posted 6 years ago

Bob -- Still knocking around with all of this?

POSTED BY: Andreas Agas
Posted 6 years ago

Andreas, I'm still knocking around and still have the same gmail address if you want to write. Your old address no longer is active.

POSTED BY: Robert Rimmer
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