Advanced Search
MyIDEAS: Login to save this article or follow this journal

Solution Of The Extended Cir Term Structure And Bond Option Valuation


Author Info

  • Yoosef Maghsoodi
Registered author(s):


    The extended Cox-Ingersoll-Ross (ECIR) models of interest rates allow for time-dependent parameters in the CIR square-root model. This article presents closed-form pathwise unique solutions of these unsolved stochastic differential equations (s.d.e.s) in terms of functionals of their driving Brownian motion and parameters. It is shown that quadratics in solution of linear s.d.e.s solve the ECIR model if and only if the "dimension" of the model is a positive integer and that this solution can be achieved by construction of a pathwise unique "generalized" Ornstein-Uhlenbeck process from the ECIR Brownian motion. For real valued dimensions an extension of the time-change theorem of Dubins and Schwarz (1965) is presented and applied to show that a lognormal process solves the model through a stochastic time change. Pathwise equivalence to a rescaled time-changed Bessel square process is also established. These novel results are applied to characterize zero-hitting time and to produce transition density and zero-hitting conditions for the ECIR spot rate. the CIR term structure is then extended to ECIR under no arbitrage, and its solutions and the transition density are represented under a new ECIR martingale measure. the findings are employed to derive a closed-form ECIR bond option valuation formula which generalizes that obtained by CIR (1985). Copyright 1996 Blackwell Publishers.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL:
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 6 (1996)
    Issue (Month): 1 ()
    Pages: 89-109

    as in new window
    Handle: RePEc:bla:mathfi:v:6:y:1996:i:1:p:89-109

    Contact details of provider:
    Web page:

    Order Information:

    Related research



    No references listed on IDEAS
    You can help add them by filling out this form.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as in new window

    Cited by:
    1. Christian Gourieroux & Alain Monfort, 2007. "Quadratic Stochastic Intensity and Prospective Mortality Tables," Working Papers 2007-30, Centre de Recherche en Economie et Statistique.
    2. Antonio Mannolini & Carlo Mari & Roberto Ren�, 2008. "Pricing caps and floors with the extended CIR model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 13(4), pages 386-400.
    3. Angelos Dassios & Jayalaxshmi Nagaradjasarma, 2006. "The square-root process and Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 337-347.
    4. Egorov, Alexei V. & Li, Haitao & Xu, Yuewu, 2003. "Maximum likelihood estimation of time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 114(1), pages 107-139, May.
    5. Choi, Seungmoon, 2013. "Closed-form likelihood expansions for multivariate time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 174(2), pages 45-65.
    6. Griselda Deelstra, 2000. "Long-term returns in stochastic interest rate models: applications," ULB Institutional Repository 2013/7590, ULB -- Universite Libre de Bruxelles.
    7. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, October.
    8. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
    9. Angelos Dassios & Jayalaxshmi Nagaradjasarma, 2011. "Pricing of Asian options on interest rates in the CIR model," LSE Research Online Documents on Economics 32084, London School of Economics and Political Science, LSE Library.
    10. Griselda Deelstra, 1999. "Yield option pricing in the generalized Cox-Ingersoll-Ross Model," ULB Institutional Repository 2013/7592, ULB -- Universite Libre de Bruxelles.
    11. Guarin, Alexander & Liu, Xiaoquan & Ng, Wing Lon, 2014. "Recovering default risk from CDS spreads with a nonlinear filter," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 87-104.
    12. D. Duffie & D. Filipovic & W. Schachermayer, 2002. "Affine Processes and Application in Finance," NBER Technical Working Papers 0281, National Bureau of Economic Research, Inc.
    13. Li, Da-Ye & Nishimura, Yusaku & Men, Ming, 2014. "Fractal markets: Liquidity and investors on different time horizons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 144-151.
    14. Erik Schlogl & Lutz Schlogl, 2000. "A square root interest rate model fitting discrete initial term structure data," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(3), pages 183-209.
    15. Guo, Zhi Jun, 2008. "A note on the CIR process and the existence of equivalent martingale measures," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 481-487, April.
    16. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.


    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:bla:mathfi:v:6:y:1996:i:1:p:89-109. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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