IDEAS home Printed from https://ideas.repec.org/p/rdg/icmadp/icma-dp2002-18.html
   My bibliography  Save this paper

Common Correlation and Calibrating the Lognormal Forward Rate Model

Author

Listed:
  • Carol Alexandra

    (ICMA Centre, University of Reading)

Abstract

1997 three papers that introduced very similar lognormal diffusion processes for interest rates appeared virtuously simultaneously. These models, now commonly called the 'LIBOR models' are based on either lognormal diffusions of forward rates as in Brace, Gatarek & Musiela (1997) and Miltersen, Sandermann & Sondermann (1997) or lognormal diffusions of swap rates, as in Jamshidian (1997). The consequent research interest in the calibration of the LIBOR models has engendered a growing empirical literature, including many papers by Brigo and Mercurio, and Riccardo Rebonato (www.fabiomercurio.it and www.damianobrigo.it and www.rebonato.com). The art of model calibration requires a reasonable knowledge of option pricing and a thorough background in statistics - techniques that are quite different to those required to design no-arbitrage pricing models. Researchers will find the book by Brigo and Mercurio (2001) and the forthcoming book by Rebonato (2002) invaluable aids to their understanding.

Suggested Citation

  • Carol Alexandra, 2002. "Common Correlation and Calibrating the Lognormal Forward Rate Model," ICMA Centre Discussion Papers in Finance icma-dp2002-18, Henley Business School, University of Reading, revised Jan 2003.
    • Handle: RePEc:rdg:icmadp:icma-dp2002-18
    as

    Download full text from publisher

    File URL: http://www.icmacentre.ac.uk/pdf/discussion/DP2002-18.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. de Jong, F.C.J.M. & Driessen, J.J.A.G. & Pelsser, A., 2000. "Libor and Swap Market Models for the Pricing of Interest Rate Derivatives : An Empirical Analysis," Discussion Paper 2000-35, Tilburg University, Center for Economic Research.
    3. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    4. Lars E.O. Svensson, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992 - 1994," NBER Working Papers 4871, National Bureau of Economic Research, Inc.
    5. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1996. "Implied Volatility Functions: Empirical Tests," Working Papers hal-00606071, HAL.
    6. Carol Alexander & Dimitri Lvov, 2003. "Statistical Properties of Forward Libor Rates," ICMA Centre Discussion Papers in Finance icma-dp2003-03, Henley Business School, University of Reading.
    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. Carol Alexander & Dimitri Lvov, 2003. "Statistical Properties of Forward Libor Rates," ICMA Centre Discussion Papers in Finance icma-dp2003-03, Henley Business School, University of Reading.
    2. S. Galluccio & J.‐M. Ly & Z. Huang & O. Scaillet, 2007. "Theory And Calibration Of Swap Market Models," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 111-141, January.
    3. Christiansen, Charlotte & Strunk Hansen, Charlotte, 2000. "Implied Volatility of Interest Rate Options: An Empirical Investigation of the Market Model," Finance Working Papers 00-1, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    4. Kokholm, Thomas, 2008. "Pricing of Traffic Light Options and other Correlation Derivatives," Finance Research Group Working Papers F-2008-01, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    5. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    6. Frank De Jong & Joost Driessen & Antoon Pelsser, 2001. "Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis," Review of Finance, European Finance Association, vol. 5(3), pages 201-237.
    7. Ernst Eberlein & Nataliya Koval, 2006. "A cross-currency Levy market model," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 465-480.
    8. Reik Borger & Jan van Heys, 2010. "Calibration of the Libor Market Model Using Correlations Implied by CMS Spread Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(5), pages 453-469.
    9. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410, July.
    10. Glasserman, P. & Zhao, X., 1998. "Arbitrage-Free Discretization of Lognormal Forward Libor and Swap Rate Models," Papers 98-09, Columbia - Graduate School of Business.
    11. Linlin Xu & Giray Ökten, 2015. "High-performance financial simulation using randomized quasi-Monte Carlo methods," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1425-1436, August.
    12. Wolfgang Kluge & Antonis Papapantoleon, 2009. "On the valuation of compositions in L\'evy term structure models," Papers 0902.3456, arXiv.org.
    13. 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.
    14. Massoud Heidari & Liuren Wu, 2002. "Term Structure of Interest Rates, Yield Curve Residuals, and the Consistent Pricing of Interest Rates and Interest Rate Derivatives," Finance 0207010, University Library of Munich, Germany, revised 10 Sep 2002.
    15. Muhammad Omer & Jakob de Haan & Bert Scholtens, 2014. "Testing uncovered interest rate parity using LIBOR," Applied Economics, Taylor & Francis Journals, vol. 46(30), pages 3708-3723, October.
    16. Takashi Yasuoka, 2001. "Mathematical Pseudo-Completion Of The Bgm Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 375-401.
    17. Andersen, Leif & Andreasen, Jesper, 2001. "Factor dependence of Bermudan swaptions: fact or fiction?," Journal of Financial Economics, Elsevier, vol. 62(1), pages 3-37, October.
    18. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6, July-Dece.
    19. Lixin Wu & Fan Zhang, 2008. "Fast swaption pricing under the market model with a square-root volatility process," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 163-180.
    20. Xu Chenglong & Guan Wei & Liang Yijuan, 2015. "A Comparison of Control Variate Methods for Pricing Interest Rate Derivatives in the LIBOR Market Model," Journal of Systems Science and Information, De Gruyter, vol. 3(1), pages 48-58, February.

    More about this item

    Statistics

    Access and download statistics

    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:rdg:icmadp:icma-dp2002-18. 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: Marie Pearson (email available below). General contact details of provider: https://edirc.repec.org/data/bsrdguk.html .

    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.