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Financial Signal Processing: A Self Calibrating Model

Author

Listed:
  • ROBERT J. ELLIOTT

    (Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1, Canada)

  • WILLIAM C. HUNTER

    (Federal Reserve Bank, 230 South LaSalle St., Chicago, Illinois 60604, USA)

  • BARBARA M. JAMIESON

    (Department of Finance and Management Science, University of Alberta, Edmonton, Alberta, Canada T6G 2G1, Canada)

Abstract

Previous work on multifactor term structure models has proposed that the short rate process is a function of some unobserved diffusion process. We consider a model in which the short rate process is a function of a Markov chain which represents the "state of the world". This enables us to obtain explicit expressions for the prices of zero-coupon bonds and other securities. Discretizing our model allows the use of signal processing techniques from Hidden Markov Models. This means we can estimate not only the unobserved Markov chain but also the parameters of the model, so the model is self-calibrating. The estimation procedure is tested on a selection of U.S. Treasury bills and bonds.

Suggested Citation

  • Robert J. Elliott & William C. Hunter & Barbara M. Jamieson, 2001. "Financial Signal Processing: A Self Calibrating Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 567-584.
    • Handle: RePEc:wsi:ijtafx:v:04:y:2001:i:04:n:s0219024901001140
    DOI: 10.1142/S0219024901001140
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    Citations

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    Cited by:

    1. Date, Paresh & Mamon, Rogemar & Tenyakov, Anton, 2013. "Filtering and forecasting commodity futures prices under an HMM framework," Energy Economics, Elsevier, vol. 40(C), pages 1001-1013.
    2. Robert Elliott & Tak Siu, 2010. "On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy," Annals of Operations Research, Springer, vol. 176(1), pages 271-291, April.
    3. Leunglung Chan & Song-Ping Zhu, 2021. "An Analytic Approach for Pricing American Options with Regime Switching," JRFM, MDPI, vol. 14(5), pages 1-20, April.
    4. Leunglung Chan & Song-Ping Zhu, 2014. "An exact and explicit formula for pricing Asian options with regime switching," Papers 1407.5091, arXiv.org.
    5. Zbigniew Palmowski & {L}ukasz Stettner & Anna Sulima, 2018. "Optimal portfolio selection in an It\^o-Markov additive market," Papers 1806.03496, arXiv.org.
    6. Christina Erlwein & Rogemar Mamon, 2009. "An online estimation scheme for a Hull–White model with HMM-driven parameters," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(1), pages 87-107, March.
    7. Tian, Ping & Zhou, Hang & Zhou, Duotai, 2023. "Analysis about the Black-Scholes asset price under the regime-switching framework," International Review of Financial Analysis, Elsevier, vol. 88(C).
    8. Xiaojing Xi & Rogemar Mamon, 2014. "Capturing the Regime-Switching and Memory Properties of Interest Rates," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 307-337, October.
    9. Zbigniew Palmowski & Łukasz Stettner & Anna Sulima, 2019. "Optimal Portfolio Selection in an Itô–Markov Additive Market," Risks, MDPI, vol. 7(1), pages 1-32, March.

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