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Consistent Re-Calibration of the Discrete-Time Multifactor Vasiček Model

Author

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  • Philipp Harms

    (Institute of Mathematics, Albert Ludwigs University of Freiburg, 79104 Freiburg, Germany)

  • David Stefanovits

    (Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland)

  • Josef Teichmann

    (Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland)

  • Mario V. Wüthrich

    (Department of Mathematics, RiskLab, ETH Zurich, 8092 Zurich, Switzerland
    Swiss Finance Institute SFI, Walchestrasse 9, 8006 Zurich, Switzerland)

Abstract

The discrete-time multifactor Vasiček model is a tractable Gaussian spot rate model. Typically, two- or three-factor versions allow one to capture the dependence structure between yields with different times to maturity in an appropriate way. In practice, re-calibration of the model to the prevailing market conditions leads to model parameters that change over time. Therefore, the model parameters should be understood as being time-dependent or even stochastic. Following the consistent re-calibration (CRC) approach, we construct models as concatenations of yield curve increments of Hull–White extended multifactor Vasiček models with different parameters. The CRC approach provides attractive tractable models that preserve the no-arbitrage premise. As a numerical example, we fit Swiss interest rates using CRC multifactor Vasiček models.

Suggested Citation

  • Philipp Harms & David Stefanovits & Josef Teichmann & Mario V. Wüthrich, 2016. "Consistent Re-Calibration of the Discrete-Time Multifactor Vasiček Model," Risks, MDPI, vol. 4(3), pages 1-31, June.
    • Handle: RePEc:gam:jrisks:v:4:y:2016:i:3:p:18-:d:72593
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Kladívko, Kamil & Rusý, Tomáš, 2023. "Maximum likelihood estimation of the Hull–White model," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 227-247.

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