I'm building a spot curve for US Treasuries. My original selection of cash treasury include all the on-the-run bills, notes, bonds from 6 months to 30 years, as well as some selected off-the-run instruments to fill in-between the on-the-runs.
Because US treasury stopped issuing 30 year cash for around 5 years in the early 2000s, there is a gap in the yield curve roughly between 15 year and 20 year maturities. I did the best I can by providing 14 year and 20 year off-the-run in the original selection. My 14 selection is (in years): 0.5, 1, 1.5, 2, 3, 5, 7, 10, 12, 14, 20, 23, 27, 30.
My question is, if I interpolate this curve, the method of interpolation will have a non-trivial effect on the shape of the curve due to the gap. Therefore when I bootstrap my spot curve based off of coupon yield, the interpolation technique on the long end of the coupon curve builds into the long end spot rate.
So far I've tried Linear Interpolation and Piecewise Cubic Hermite Interpolating Polynomial. I think the Fed Reserve publish their daily yield curve off of the second kind.
Lastly, can someone critique whatever I've said if they have any better idea? My spot curve using PCHIP method on coupon yield curve is drawn below. The spot curve was also interpolated into 1-month interval using PCHIP. I just feel odd looking at this because of the sudden curvature change around 12 year to 22 year sector. If someone thinks this is a good approximation for how the yield curve should look like fundamentally, I would love to hear your explanation. I sincerely apologize for so many questions.