Yield Curves: Bridging the P-Q Modeling Divide

Check it out:

"Bridging the P-Q Modeling Divide with the Factor-HJM Modeling Framework"
by
Andrei Lyashenko and Yevgeny Goncharov.

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3995533

Really nice work.

I chuckled when I noticed that it characterizes a significant part of its contribution as solving the "mystery behind the very peculiar form of the mean reversion matrices" used to produce the arbitrage-free Nelson-Siegel (AFNS) yield-curve model of Christensen, Diebold and Rudebusch (CDR:  2009, 2011).  Of course the CDR mean reversion matrices are not "peculiar" in any negative sense, but they are definitely special, delivering precisely what is needed to enforce absence of arbitrage.  Admittedly, we may have presented them as if pulled from a hat.  In fact we arrived at them by reverse engineering, that is, by the venerable (and iterative) strategy of "guess and verify".  

The new Lyashenko-Goncharovnew paper arrives at the CDR mean reversion matrices in a more constructive fashion, in an impressively broad and unifying framework that bridges dynamic factor yield curve models, Heath-Jarrow-Morton forward curve models, and Duffie-Kan affine arbitrage-free models.  In so doing, it further cements the central status of AFNS, now transcending sub-disciplines.