I have constant maturity treasury data from the h15 release of the FED, from which I use 6 month, 1 year, 2, 3, 5, 7, 10, and 20 year yields. I want to strip the zero coupon curve, but am not sure about the best (most accurate) way to fill in the missing maturities for the CMT yields, which I need before I can bootstrap the zero coupon curve. Is there anyone that can provide me with some references on the different techniques that can be used, that are also understandable for application?
The CMT yields published by the Fed/US Treasury are par yields calculated using a cubic spline model. In other words, these are the yields to maturity as well as coupon rates on bonds whose theoretic prices are 100. With this information in mind, you can linearly interpolate between these yields, or use a cubic spline to fill in rates at other tenors, assuming the filled-in rates are also par yields, and bootstrap this resulting "par yield curve."
A better approach would be to use a large number of off-the-run Treasuries and fit a spline through them. Fed researchers provide an implementation of the Svensson model. The methodology, along with the fitted yield curve data (including zero coupon rates), are available here.