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Long Term Risk: A Martingale Approach

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  • Likuan Qin
  • Vadim Linetsky

Abstract

This paper extends the long-term factorization of the stochastic discount factor introduced and studied by Alvarez and Jermann (2005) in discretetime ergodic environments and by Hansen and Scheinkman (2009) and Hansen (2012) in Markovian environments to general semimartingale environments. The transitory component discounts at the stochastic rate of return on the long bond and is factorized into discounting at the long-term yield and a positive semimartingale that extends the principal eigenfunction of Hansen and Scheinkman (2009) to the semimartingale setting. The permanent component is a martingale that accomplishes a change of probabilities to the long forward measure, the limit of T-forward measures. The change of probabilities from the data generating to the long forward measure absorbs the long-term risk-return trade-off and interprets the latter as the long-term risk-neutral measure.

Suggested Citation

  • Likuan Qin & Vadim Linetsky, 2014. "Long Term Risk: A Martingale Approach," Papers 1411.3078, arXiv.org, revised Oct 2016.
    • Handle: RePEc:arx:papers:1411.3078
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    Cited by:

    1. Likuan Qin & Vadim Linetsky, 2016. "Long-Term Factorization of Affine Pricing Kernels," Papers 1610.00778, arXiv.org, revised Jul 2017.
    2. Likuan Qin & Vadim Linetsky, 2016. "The Long Bond, Long Forward Measure and Long-Term Factorization in Heath-Jarrow-Morton Models," Papers 1610.00818, arXiv.org, revised Jul 2017.

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