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Model for Pricing Zero-Coupon Treasury Bonds

Posted 5 years ago
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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.

http://pages.suddenlink.net/rhr/fin07/TreasuryZeroes.html

Or the Mathematica notebook containing all the functions can be opened with the following line of code:
NotebookPut@Import["http://pages.suddenlink.net/rhr/fin07/TreasuryZeroes.nb"];
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
3 Replies
Posted 5 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.

Bob -- Still knocking around with all of this?

Posted 8 months 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.

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