If you have a chance, I would be curious is that holds.

This form makes it much clearer. Thx. Now shouldn’t the c/gamma variable in the inflation model then be negative as well?

This is the way I have written the from the beginning. I said a, b, c, and w before — originally they were alpha, beta, gamma and omega. It is a remarkably flexible functional form, and parsimonious. If omega is one (rare), beta and gamma become the prices for duration and convexity. Alpha is the overnight rate. Since omega is usually not one, I call beta and gamma the prices of pseudo-duration and pseudo-convexity. Under ordinary circumstances, for nominal rates, alpha, beta and omega are positive, and gamma negative.

Things are not normal for alpha now, given the government flooding the system with liquidity. Alpha would go more negative if I did not constrain spot rates after three months to be positive. I would get a better fit, but I have a hard time thinking that model is working right if I let spot rates get negative too far out.

The omega variable is what makes the functional form so flexible. It also means that the parameters can no longer be estimated through regression, but must be solved using nonlinear optimization (in Excel, using solver).

The raw data for the model is nominal Treasury note and bond, and TIPS prices. I minimize the squared error between the actual prices, and the hypothetical prices generated by discounting the cash flows of the bonds from the yields generated from the four-factor equation above. A second four-factor equation of the same form drives forward inflation estimates, and thus cash flows on the TIPS.

So, there are eight variables for this model. It’s a parsimonious system that explains a lot, and looks reasonable.

David C. — I might have a copy of the paper somewhere in my basement. If I find it, I could scan it. My problem is getting the time to look for it. If you have the formula that I listed, you have the “money shot” of the paper.

There are two sets of a, b, c, and w. One for nominal Treasury rates, and the other for inflation. Eight parameters in all.

What was the data? Bond prices, coupons, and maturities and time. The idea was to estimate interest rates and implied inflation rates from the prices of Treasury securities versus their cash flows.

S. Diller, “The yield surface – a three dimensional approach relating yield to duration and convexity, Bear Stearns, fixed income strategies” February, New York

Is there any way we can get a copy of this paper? It doesn’t appear to be published in any journals I can find.

I am a CFA candidate and would like to learn quantitative techniques in detail, that are used in Investment Decision Making. Could you please suggest some books that covers relevant areas??

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With Regards,