IDEAS home Printed from https://ideas.repec.org/a/spr/sistpr/v18y2015i3p293-313.html
   My bibliography  Save this article

Stability of the filter with Poisson observations

Author

Listed:
  • Zhiqiang Li
  • Jie Xiong

Abstract

The short interest rate process is modeled by a diffusion process $$X(t)$$ X ( t ) . With the counting process observations, a filtering problem is formulated and its exponential stability is derived when the process $$X(t)$$ X ( t ) is asymptotically stationary. Copyright Springer Science+Business Media Dordrecht 2015

Suggested Citation

  • Zhiqiang Li & Jie Xiong, 2015. "Stability of the filter with Poisson observations," Statistical Inference for Stochastic Processes, Springer, vol. 18(3), pages 293-313, October.
  • Handle: RePEc:spr:sistpr:v:18:y:2015:i:3:p:293-313
    DOI: 10.1007/s11203-014-9114-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11203-014-9114-5
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s11203-014-9114-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Jie Xiong & Yong Zeng, 2011. "A branching particle approximation to a filtering micromovement model of asset price," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 111-140, May.
    3. T. Duncan & B. Pasik-Duncan & L. Stettner, 2005. "Ergodic and adaptive control of hidden Markov models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 297-318, November.
    4. Michael A. Kouritzin & Yong Zeng, 2005. "Bayesian Model Selection Via Filtering For A Class Of Micro-Movement Models Of Asset Price," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 97-121.
    5. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    6. Rendleman, Richard J. & Bartter, Brit J., 1980. "The Pricing of Options on Debt Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(1), pages 11-24, March.
    7. Papavasiliou, Anastasia, 2006. "Parameter estimation and asymptotic stability in stochastic filtering," Stochastic Processes and their Applications, Elsevier, vol. 116(7), pages 1048-1065, July.
    8. Budhiraja, A. & Ocone, D., 1999. "Exponential stability in discrete-time filtering for non-ergodic signals," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 245-257, August.
    9. Yong Zeng, 2003. "A Partially Observed Model for Micromovement of Asset Prices with Bayes Estimation via Filtering," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 411-444, July.
    10. Kiseop Lee & Yong Zeng, 2010. "Risk Minimization for a Filtering Micromovement Model of Asset Price," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(2), pages 177-199.
    11. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    12. Hasbrouck, Joel, 2002. "Stalking the "efficient price" in market microstructure specifications: an overview," Journal of Financial Markets, Elsevier, vol. 5(3), pages 329-339, July.
    13. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704.
    14. LeGland, François & Oudjane, Nadia, 2003. "A robustification approach to stability and to uniform particle approximation of nonlinear filters: the example of pseudo-mixing signals," Stochastic Processes and their Applications, Elsevier, vol. 106(2), pages 279-316, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Prakash Chakraborty & Kiseop Lee, 2022. "Bond Prices Under Information Asymmetry and a Short Rate with Instantaneous Feedback," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 613-634, June.
    2. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    3. repec:uts:finphd:40 is not listed on IDEAS
    4. Michael J. Tomas & Jun Yu, 2021. "An Asymptotic Solution for Call Options on Zero-Coupon Bonds," Mathematics, MDPI, vol. 9(16), pages 1-23, August.
    5. Zura Kakushadze, 2015. "Coping with Negative Short-Rates," Papers 1502.06074, arXiv.org, revised Aug 2015.
    6. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018, January-A.
    7. Bali, Turan G., 2003. "Modeling the stochastic behavior of short-term interest rates: Pricing implications for discount bonds," Journal of Banking & Finance, Elsevier, vol. 27(2), pages 201-228, February.
    8. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, August.
    9. Miloš Kopa & Vittorio Moriggia & Sebastiano Vitali, 2018. "Individual optimal pension allocation under stochastic dominance constraints," Annals of Operations Research, Springer, vol. 260(1), pages 255-291, January.
    10. Yedidya Rabinovitz, 2017. "A new S.D.E. and instantaneous mean reversion rate formula (presented via a numerical empirical model comparison)," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-22, June.
    11. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    12. Álvarez Echeverría Francisco & López Sarabia Pablo & Venegas Martínez Francisco, 2012. "Valuación financiera de proyectos de inversión en nuevas tecnologías con opciones reales," Contaduría y Administración, Accounting and Management, vol. 57(3), pages 115-145, julio-sep.
    13. Matsumura, Marco & Moreira, Ajax & Vicente, José, 2011. "Forecasting the yield curve with linear factor models," International Review of Financial Analysis, Elsevier, vol. 20(5), pages 237-243.
    14. Lin, Bing-Huei, 1999. "Fitting the term structure of interest rates for Taiwanese government bonds," Journal of Multinational Financial Management, Elsevier, vol. 9(3-4), pages 331-352, November.
    15. Gollier, Christian, 2002. "Time Horizon and the Discount Rate," Journal of Economic Theory, Elsevier, vol. 107(2), pages 463-473, December.
    16. Yang, Nian & Chen, Nan & Wan, Xiangwei, 2019. "A new delta expansion for multivariate diffusions via the Itô-Taylor expansion," Journal of Econometrics, Elsevier, vol. 209(2), pages 256-288.
    17. Kimmel, Robert L., 2004. "Modeling the term structure of interest rates: A new approach," Journal of Financial Economics, Elsevier, vol. 72(1), pages 143-183, April.
    18. Ben S. Bernanke & Vincent R. Reinhart & Brian P. Sack, 2004. "Monetary Policy Alternatives at the Zero Bound: An Empirical Assessment," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 35(2), pages 1-100.
    19. Huse, Cristian, 2011. "Term structure modelling with observable state variables," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3240-3252.
    20. Levendorskii, Sergei, 2004. "Consistency conditions for affine term structure models," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 225-261, February.
    21. Nowman, K. Ben & Sorwar, Ghulam, 2005. "Derivative prices from interest rate models: results for Canada, Hong Kong, and United States," International Review of Financial Analysis, Elsevier, vol. 14(4), pages 428-438.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sistpr:v:18:y:2015:i:3:p:293-313. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.