What are the best methods to extrapolate bond yields from an existing curve that doesn't extend quite this far?
For example, how would one come about finding a theoretical bond yield for a 40 or 50 year US Treasury Bond, when no bond exists of a maturity of much more than 30 years? I guess you could remove credit risk from corporate ultra-long bonds, but this might prove difficult.
I explored using curve fitting models such as Nelson-Siegel and Svensson, but the results are a little unsatisfactory and highly volatile, with theoretical yields at the 50 year mark varying by as more than 50bps depending on the date at which the curve is calculated (over a short time frame).