Tweaking the Hussmann Interest Rate Calculation

Trying to get back to simulating an interest rate. Wanted to look at the Hussmann calc that I got from Oilfield the other week. I put the interest rate on a graph, and the Hussmann calculation.

I put another line on there, the difference between the interest rate and the Hussmann number. And then Whoa! Look at those bottoms! I eyeballed a line thru the bottoms and sure enough, they seem to drift quite reliably downward at a regular pace, over the full 68 or so years shown on the graph:

Graph #1

In other words, the red line starts out near the bottom of the blue line, and ends up near the top of the blue line. I didn't see it quite that clearly before I did the subtraction.

I got wondering if I could adjust the red line to center it better on the blue, or to position it at will I guess -- to gain control over where the green line ends up on the graph, and the slope of the black line.

I don't know what effect I get by changing the constants, the 4.27 and the 45.5 in the calculation of the red line. I have to get comfortable with what happens when I make changes to those values.

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Starting from the default values, decreasing c1 or increasing c2 makes the red line straighter without much changing the ends. Increasing c1 or decreasing c2 exaggerates the shape of the red line, again with little change at the ends.

It looks to me like I cannot turn the red line at an angle that would make the bottoms of the green "difference line" more horizontal. Therefore, the "best" I can get is pretty much what Hussmann provides, where the red line starts out low on the blue, and ends up high on it.

// Test it yourself with this Excel file