  This paper proves existence of the long bond, long forward measure and
long-term factorization of the stochastic discount factor (SDF) of Alvarez and
Jermann (2005) and Hansen and Scheinkman (2009) in Heath-Jarrow-Morton (HJM)
models in the function space framework of Filipovic (2001). A sufficient
condition on the weight in the Hilbert space of forward rate volatility curves
is given that ensures existence of the long bond volatility process, the long
bond process and the long-term factorization of the SDF into discounting at the
rate of return on the long bond and a martingale component defining the long
forward measure, the long-term limit of T-forward measures.
