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Long-term factorization in Heath–Jarrow–Morton models

Author

Listed:
  • Likuan Qin

    (Northwestern University)

  • Vadim Linetsky

    (Northwestern University)

Abstract

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 $T$ -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.

Suggested Citation

  • Likuan Qin & Vadim Linetsky, 2018. "Long-term factorization in Heath–Jarrow–Morton models," Finance and Stochastics, Springer, vol. 22(3), pages 621-641, July.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:3:d:10.1007_s00780-018-0365-7
    DOI: 10.1007/s00780-018-0365-7
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    References listed on IDEAS

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    More about this item

    Keywords

    Stochastic discount factor; Long-term factorization; Long bond; Long forward measure; HJM models;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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