Long-term factorization in Heath–Jarrow–Morton models

Likuan Qin, Vadim Linetsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The long-term factorization decomposes the stochastic discount factor (SDF) into discounting at the rate of return on the long bond and a martingale that defines a long-term forward measure. We establish sufficient conditions for existence of the long-term factorization in HJM models. A condition on the forward rate volatility ensures existence of the long bond volatility. This yields existence of the long bond and convergence of T-forward measures to the long forward measure. It contrasts with the familiar risk-neutral factorization that decomposes the SDF into discounting at the short rate and a martingale defining the risk-neutral measure.

Original languageEnglish (US)
Pages (from-to)621-641
Number of pages21
JournalFinance and Stochastics
Issue number3
StatePublished - Jul 1 2018


  • HJM models
  • Long bond
  • Long-term factorization
  • Long forward measure
  • Stochastic discount factor

ASJC Scopus subject areas

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty


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