IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i13p1469-d580240.html
   My bibliography  Save this article

New Approximations to Bond Prices in the Cox–Ingersoll–Ross Convergence Model with Dynamic Correlation

Author

Listed:
  • Beáta Stehlíková

    (Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská Dolina, 842 48 Bratislava, Slovakia)

Abstract

We study a particular case of a convergence model of interest rates. The bond prices are given as solutions of a parabolic partial differential equation and we consider different possibilities of approximating them, using approximate analytical solutions. We consider an approximation already suggested in the literature and compare it with a newly suggested one for which we derive the order of accuracy. Since the two formulae use different approaches and the resulting leading terms of the error depend on different parameter sets of the model, we propose their combination, which has a higher order of accuracy. Finally, we propose one more approach, which leads to higher accuracy of the resulting approximation formula.

Suggested Citation

  • Beáta Stehlíková, 2021. "New Approximations to Bond Prices in the Cox–Ingersoll–Ross Convergence Model with Dynamic Correlation," Mathematics, MDPI, vol. 9(13), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1469-:d:580240
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/13/1469/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/13/1469/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584, January.
    2. Moreno, Manuel & Platania, Federico, 2015. "A cyclical square-root model for the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 241(1), pages 109-121.
    3. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    4. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    5. Teresa Corzo Santamaria & E. S. Schwartz, 2000. "Convergence within the EU: Evidence from Interest Rates," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 29(2), pages 243-266, July.
    6. Fabricio Tourrucoo & Patrick S. Hagan & Gilberto F. Schleiniger, 2007. "Approximate Formulas for Zero-coupon Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(3), pages 207-226.
    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. Gregory Koutmos & George Philippatos, 2007. "Asymmetric Mean Reversion in European Interest Rates: A Two-factor Model," The European Journal of Finance, Taylor & Francis Journals, vol. 13(8), pages 741-750.
    2. Tiziana Di Matteo & Tomaso Aste, 2002. "How Does The Eurodollar Interest Rate Behave?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 107-122.
    3. Buraschi, Andrea & Jiltsov, Alexei, 2005. "Inflation risk premia and the expectations hypothesis," Journal of Financial Economics, Elsevier, vol. 75(2), pages 429-490, February.
    4. Kozicki, Sharon & Tinsley, P. A., 2001. "Shifting endpoints in the term structure of interest rates," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 613-652, June.
    5. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    6. Guo, Bin & Huang, Fuzhe & Li, Kai, 2022. "Time to build and bond risk premia," Journal of Economic Dynamics and Control, Elsevier, vol. 136(C).
    7. repec:ehu:dfaeii:6754 is not listed on IDEAS
    8. Bao, Jianhai & Yuan, Chenggui, 2013. "Long-term behavior of stochastic interest rate models with jumps and memory," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 266-272.
    9. Broze, Laurence & Scaillet, Olivier & Zakoian, Jean-Michel, 1995. "Testing for continuous-time models of the short-term interest rate," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 199-223, September.
    10. Renato França & Raquel M. Gaspar, 2023. "On the Bias of the Unbiased Expectation Theory," Mathematics, MDPI, vol. 12(1), pages 1-20, December.
    11. Moreno, Manuel, 1995. "On the term structure of Interbank interest rates: jump-diffusion processes and option pricing," DES - Working Papers. Statistics and Econometrics. WS 7074, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, May.
    13. Bu, Ruijun & Jawadi, Fredj & Li, Yuyi, 2017. "An empirical comparison of transformed diffusion models for VIX and VIX futures," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 46(C), pages 116-127.
    14. Poletti Laurini, Márcio & Moura, Marcelo, 2010. "Constrained smoothing B-splines for the term structure of interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 339-350, April.
    15. Gil-Bazo Javier & Rubio Gonzalo, 2004. "A Nonparametric Dimension Test of the Term Structure," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(3), pages 1-28, September.
    16. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    17. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    18. Giacomo Toscano & Maria Cristina Recchioni, 2022. "Bias-optimal vol-of-vol estimation: the role of window overlapping," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 137-185, June.
    19. Manuel Arapis & Jiti Gao, 2006. "Empirical Comparisons in Short-Term Interest Rate Models Using Nonparametric Methods," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 310-345.
    20. Ruijun Bu & Ludovic Giet & Kaddour Hadri & Michel Lubrano, 2009. "Modeling Multivariate Interest Rates using Time-Varying Copulas and Reducible Stochastic Differential Equations," Working Papers halshs-00408014, HAL.

    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:gam:jmathe:v:9:y:2021:i:13:p:1469-:d:580240. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.