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Principal-Component-Based Gaussian Affine Term Structure Models: Constraints And Their Financial Implications

Author

Listed:
  • RICCARDO REBONATO

    (EDHEC Business School — London 10, Fleet Place, Oxford University, OCIAM, St Giles, Morgan Stanley, 25 Cabot Square, UK)

  • IVAN SAROKA

    (EDHEC Business School — London 10, Fleet Place, Oxford University, OCIAM, St Giles, Morgan Stanley, 25 Cabot Square, UK)

  • VLAD PUTIATYN

    (EDHEC Business School — London 10, Fleet Place, Oxford University, OCIAM, St Giles, Morgan Stanley, 25 Cabot Square, UK)

Abstract

This work builds on the work by Joslin et al. [(2011) A new perspective on Gaussian dynamic term structure Models, The Review of Financial Studies 24, 926–970] on the affine dynamics of portfolios of yields and addresses the unresolved issues of ‘internal consistency’ mentioned in the same paper. It shows the unexpected constraints that have to be satisfied by the ℚ-measure evolution of the yield curve if the portfolio of yields has to be interpreted as their principal components. This choice of state variables is common in the recent literature and so our findings are intrinsically interesting. However, we show that our results also extend to a wide class of choices for state variables, when these are chosen as linear combinations of yields. We show that these constraints have important financial consequences, which, to our knowledge, have not been appreciated. In particular, this paper highlights some puzzling issues of compatibility between the ℚ- and ℙ-measure dynamics of Gaussian dynamic term structure models when principal components are chosen as state variables, once the constraints we derive are taken into account.

Suggested Citation

  • Riccardo Rebonato & Ivan Saroka & Vlad Putiatyn, 2020. "Principal-Component-Based Gaussian Affine Term Structure Models: Constraints And Their Financial Implications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-25, March.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:02:n:s0219024920500089
    DOI: 10.1142/S0219024920500089
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    References listed on IDEAS

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    1. Scott Joslin & Kenneth J. Singleton & Haoxiang Zhu, 2011. "A New Perspective on Gaussian Dynamic Term Structure Models," The Review of Financial Studies, Society for Financial Studies, vol. 24(3), pages 926-970.
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