Specifically, the US govt bond market is segmented and the shape is difficult to model in a structural model, because recently there is a maturity gap from 12 to 20 year, and the front and back ends are so different. Nelson Siegel family clearly has difficulties at long end, even more complex/time-series models do not fit quite well.
What is the latest development to term structure modelling, especially for US market?
I interpret your question to be asking about curve fitting techniques (for constructing fitted par/zero curves), since a term structure model (HW, LMM, etc.) can always be constructed to fit a given yield curve perfectly.
In an institutional setting, there really hasn't been any new models being proposed, because the existing ones are all very flexible and capable. One bulge bracket bank did improve their curve fitting technique back in 2018 – instead of optimizing for the lowest price errors, they now minimize yield errors across the curve. This is, of course, not particularly groundbreaking and most other banks/funds have been doing this for years if not decades.
We do constantly strive to improve our curve fitting techniques, but as alluded to above, the focus is generally not on which model to use. Nelson-Siegel and Svensson are not widely used outside of central banks; instead, exponential, cubic, and B-splines are the norms. These models are so flexibly and have so many degrees of freedom that we frequently revisit whether the knot points are optimally placed (particular as maturity gaps shift over time), whether the number of knot points is appropriate given market conditions, whether the right set of bonds are included in the estimation (should the new 20-year be included in the estimation set), whether fitting quality is deteriorating for the purpose at hand (are rich/cheap signals sensible). These are more art than science. What's more, the answers change as the market evolves and as institutional priority shifts (e.g., you might not care about fitting quality at the front end if your institution only trades the long end).
I did recently run into this paper Reconstructing the Yield Curve which has some interesting ideas, although admittedly I haven't replicated the technique to assess it fully.
