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Nonlinear Kalman Filtering in Affine Term Structure Models

Author

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  • Peter Christoffersen
  • Christian Dorion
  • Kris Jacobs
  • Lotfi Karoui

Abstract

The extended Kalman filter, which linearizes the relationship between security prices and state variables, is widely used in fixed income applications. We investigate if the unscented Kalman filter should be used to capture nonlinearities, and compare the performance of the Kalman filter to that of the particle filter. We analyze the cross section of swap rates, which are mildly nonlinear in the states, and cap prices, which are highly nonlinear. When caps are used to filter the states, the unscented Kalman filter significantly outperforms its extended counterpart. The unscented Kalman filter also performs well when compared to the much more computationally intensive particle filter. These findings suggest that the unscented Kalman filter may prove to be a good approach for variety of problems in fixed income pricing.

Suggested Citation

  • Peter Christoffersen & Christian Dorion & Kris Jacobs & Lotfi Karoui, 2014. "Nonlinear Kalman Filtering in Affine Term Structure Models," Cahiers de recherche 1404, CIRPEE.
  • Handle: RePEc:lvl:lacicr:1404
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    References listed on IDEAS

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    Cited by:

    1. Filipović, Damir & Gourier, Elise & Mancini, Loriano, 2016. "Quadratic variance swap models," Journal of Financial Economics, Elsevier, vol. 119(1), pages 44-68.
    2. Damien Ackerer & Damir Filipovi'c, 2016. "Linear Credit Risk Models," Papers 1605.07419, arXiv.org, revised Jan 2018.
    3. Andrea Berardi, 2013. "Inflation Risk Premia, Yield Volatility and Macro Factors," Working Papers 27/2013, University of Verona, Department of Economics.
    4. 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.
    5. 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.
    6. Jean-François Bégin, 2016. "Deflation Risk and Implications for Life Insurers," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-36, December.
    7. 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.
    8. 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.
    9. 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.

    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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