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Long‐Term Risk: A Martingale Approach

Author

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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 discrete‐time 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, 2017. "Long‐Term Risk: A Martingale Approach," Econometrica, Econometric Society, vol. 85, pages 299-312, January.
    • Handle: RePEc:wly:emetrp:v:85:y:2017:i::p:299-312
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    Cited by:

    1. Jaroslav Borovička & John Stachurski, 2020. "Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities," Journal of Finance, American Finance Association, vol. 75(3), pages 1457-1493, June.
    2. Damir Filipovic & Martin Larsson & Anders B. Trolle, 2018. "On the Relation Between Linearity-Generating Processes and Linear-Rational Models," Papers 1806.03153, arXiv.org.
    3. Dillschneider, Yannick & Maurer, Raimond, 2019. "Functional Ross recovery: Theoretical results and empirical tests," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).
    4. Borovička, Jaroslav & Stachurski, John, 2021. "Stability of equilibrium asset pricing models: A necessary and sufficient condition," Journal of Economic Theory, Elsevier, vol. 193(C).
    5. Backus, David & Boyarchenko, Nina & Chernov, Mikhail, 2018. "Term structures of asset prices and returns," Journal of Financial Economics, Elsevier, vol. 129(1), pages 1-23.
    6. Armerin, Fredrik, 2019. "Stochastic discount factors and the optimal timing of irreversible investments," Working Paper Series 19/11, Royal Institute of Technology, Department of Real Estate and Construction Management & Banking and Finance.
    7. Dorje C. Brody & Lane P. Hughston & David M. Meier, 2016. "L\'evy-Vasicek Models and the Long-Bond Return Process," Papers 1608.06376, arXiv.org, revised Sep 2016.
    8. Jensen, Christian Skov & Lando, David & Pedersen, Lasse Heje, 2019. "Generalized recovery," Journal of Financial Economics, Elsevier, vol. 133(1), pages 154-174.
    9. Neuhierl, Andreas & Varneskov, Rasmus T., 2021. "Frequency dependent risk," Journal of Financial Economics, Elsevier, vol. 140(2), pages 644-675.
    10. Choi, Kyoung Jin & Jeon, Junkee & Koo, Hyeng Keun, 2022. "Intertemporal preference with loss aversion: Consumption and risk-attitude," Journal of Economic Theory, Elsevier, vol. 200(C).
    11. Mirela Sandulescu & Fabio Trojani & Andrea Vedolin, 2021. "Model‐Free International Stochastic Discount Factors," Journal of Finance, American Finance Association, vol. 76(2), pages 935-976, April.
    12. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2019. "Gauge transformations in the dual space, and pricing and estimation in the long run in affine jump-diffusion models," Papers 1912.06948, arXiv.org, revised Dec 2019.

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