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Nonlinear Kalman Filtering in Affine Term Structure Models

Author

Listed:
  • Peter Christoffersen

    () (University of Toronto - Rotman School of Management and CREATES)

  • Christian Dorion

    () (HEC Montreal)

  • Kris Jacobs

    () (University of Houston and Tilburg University)

  • Lotfi Karoui

    () (Goldman, Sachs & Co.)

Abstract

When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi?ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze the potential of the unscented Kalman ?filter to properly capture nonlinearities. To illustrate the advantages of the unscented Kalman ?filter, we analyze the cross section of swap rates, which are relatively simple non-linear instruments, and cap prices, which are highly nonlinear in the states. An extensive Monte Carlo experiment demonstrates that the unscented Kalman fi?lter is much more accurate than its extended counterpart in fi?ltering the states and forecasting swap rates and caps. Our fi?ndings suggest that the unscented Kalman fi?lter may prove to be a good approach for a number of other problems in fi?xed income pricing with nonlinear relationships between the state vector and the observations, such as the estimation of term structure models using coupon bonds and the estimation of quadratic term structure models.

Suggested Citation

  • Peter Christoffersen & Christian Dorion & Kris Jacobs & Lotfi Karoui, 2012. "Nonlinear Kalman Filtering in Affine Term Structure Models," CREATES Research Papers 2012-49, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2012-49
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    References listed on IDEAS

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    Cited by:

    1. Dubecq, Simon & Monfort, Alain & Renne, Jean-Paul & Roussellet, Guillaume, 2016. "Credit and liquidity in interbank rates: A quadratic approach," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 29-46.
    2. Kiesel, Rüdiger & Rahe, Florentin, 2017. "Option pricing under time-varying risk-aversion with applications to risk forecasting," Journal of Banking & Finance, Elsevier, vol. 76(C), pages 120-138.
    3. Damien Ackerer & Damir Filipovi'c, 2016. "Linear Credit Risk Models," Papers 1605.07419, arXiv.org, revised Jan 2018.
    4. Andrea Berardi, 2013. "Inflation Risk Premia, Yield Volatility and Macro Factors," Working Papers 27/2013, University of Verona, Department of Economics.
    5. esposito, francesco paolo & cummins, mark, 2015. "Filtering and likelihood estimation of latent factor jump-diffusions with an application to stochastic volatility models," MPRA Paper 64987, University Library of Munich, Germany.
    6. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    7. Filipović, Damir & Gourier, Elise & Mancini, Loriano, 2016. "Quadratic variance swap models," Journal of Financial Economics, Elsevier, vol. 119(1), pages 44-68.
    8. Boudreault, Mathieu & Gauthier, Geneviève & Thomassin, Tommy, 2015. "Estimation of correlations in portfolio credit risk models based on noisy security prices," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 334-349.
    9. Jean-François Bégin, 2016. "Deflation Risk and Implications for Life Insurers," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-36, December.

    More about this item

    Keywords

    Kalman filtering; nonlinearity; term structure models; swaps; caps.;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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