IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v21y2018i04ns0219024918500206.html
   My bibliography  Save this article

Efficient Long-Dated Swaption Volatility Approximation In The Forward-Libor Model

Author

Listed:
  • JACQUES VAN APPEL

    (Faculty of Science, Department of Statistics, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, South Africa)

  • THOMAS A. MCWALTER

    (The African Institute of Financial Markets and Risk Management, University of Cape Town, Private Bag X3, Rondebosch, 7701, South Africa3Faculty of Economic and Financial Sciences, Department of Finance & Investment Management, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, South Africa)

Abstract

We provide efficient swaption volatility approximations for longer maturities and tenors under the lognormal forward-LIBOR model (LFM). In particular, we approximate the swaption volatility with a mean update of the spanning forward rates. Since the joint distribution of the forward rates is not known under a typical pricing measure, we resort to numerical discretization techniques. More specifically, we approximate the mean forward rates with a multi-dimensional weak order 2.0 Itō–Taylor scheme. The higher-order terms allow us to more accurately capture the state dependence in the drift terms and compute conditional expectations with second-order accuracy. We test our approximations for longer maturities and tenors using a quasi-Monte Carlo (QMC) study and find them to be substantially more effective when compared to the existing approximations, particularly for calibration purposes.

Suggested Citation

  • Jacques Van Appel & Thomas A. Mcwalter, 2018. "Efficient Long-Dated Swaption Volatility Approximation In The Forward-Libor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-26, June.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:04:n:s0219024918500206
    DOI: 10.1142/S0219024918500206
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024918500206
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024918500206?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. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
    3. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
    4. Tim Dun & Geoff Barton & Erik Schlögl, 2001. "Simulated Swaption Delta–Hedging In The Lognormal Forward Libor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 677-709.
    5. Atsushi Kawai, 2003. "A new approximate swaption formula in the LIBOR market model: an asymptotic expansion approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 49-74.
    6. Damiano Brigo & Jan Liinev, 2005. "On the distributional distance between the lognormal LIBOR and swap market models," Quantitative Finance, Taylor & Francis Journals, vol. 5(5), pages 433-442.
    7. John Schoenmakers & Brian Coffey, 2003. "Systematic Generation of Parametric Correlation Structures for the LIBOR Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(05), pages 507-519.
    8. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    9. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. He, Jie-Cao & Hsieh, Chang-Chieh & Huang, Zi-Wei & Lin, Shih-Kuei, 2023. "Valuation of callable range accrual linked to CMS Spread under generalized swap market model," International Review of Financial Analysis, Elsevier, vol. 90(C).

    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. Jaka Gogala & Joanne E. Kennedy, 2017. "CLASSIFICATION OF TWO- AND THREE-FACTOR TIME-HOMOGENEOUS SEPARABLE LMMs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-44, March.
    2. Raoul Pietersz & Marcel Regenmortel, 2006. "Generic market models," Finance and Stochastics, Springer, vol. 10(4), pages 507-528, December.
      • Pietersz, R. & van Regenmortel, M., 2005. "Generic Market Models," ERIM Report Series Research in Management ERS-2005-010-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
      • Raoul Pietersz & Marcel van Regenmortel, 2005. "Generic Market Models," Finance 0502009, University Library of Munich, Germany.
    3. Nicolas Merener & Paul Glasserman, 2003. "Numerical solution of jump-diffusion LIBOR market models," Finance and Stochastics, Springer, vol. 7(1), pages 1-27.
    4. 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.
    5. Pierre-Edouard Arrouy & Sophian Mehalla & Bernard Lapeyre & Alexandre Boumezoued, 2020. "Jacobi Stochastic Volatility factor for the Libor Market Model," Working Papers hal-02468583, HAL.
    6. Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2011. "Efficient and accurate log-Lévi approximations to Lévi driven LIBOR models," CREATES Research Papers 2011-22, Department of Economics and Business Economics, Aarhus University.
    7. Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2011. "Efficient and accurate log-L\'evy approximations to L\'evy driven LIBOR models," Papers 1106.0866, arXiv.org, revised Jan 2012.
    8. Heidari, Massoud & Wu, Liuren, 2009. "A Joint Framework for Consistently Pricing Interest Rates and Interest Rate Derivatives," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(3), pages 517-550, June.
    9. K. F. Pilz & E. Schlögl, 2013. "A hybrid commodity and interest rate market model," Quantitative Finance, Taylor & Francis Journals, vol. 13(4), pages 543-560, March.
    10. Zühlsdorff, Christian, 2002. "Extended Libor Market Models with Affine and Quadratic Volatility," Bonn Econ Discussion Papers 6/2002, University of Bonn, Bonn Graduate School of Economics (BGSE).
    11. 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.
    12. Glasserman, P. & Zhao, X., 1998. "Arbitrage-Free Discretization of Lognormal Forward Libor and Swap Rate Models," Papers 98-09, Columbia - Graduate School of Business.
    13. Da Fonseca, José & Gnoatto, Alessandro & Grasselli, Martino, 2013. "A flexible matrix Libor model with smiles," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 774-793.
    14. Erik Schlögl, 2001. "Arbitrage-Free Interpolation in Models of Market Observable Interest Rates," Research Paper Series 71, Quantitative Finance Research Centre, University of Technology, Sydney.
    15. Svenstrup, Mikkel, 2005. "On the suboptimality of single-factor exercise strategies for Bermudan swaptions," Journal of Financial Economics, Elsevier, vol. 78(3), pages 651-684, December.
    16. Kenichiro Shiraya & Akihiko Takahashi & Akira Yamazaki, 2010. "Pricing Swaptions under the Libor Market Model of Interest Rates with Local-Stochastic Volatility Models," CARF F-Series CARF-F-214, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    17. 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.
    18. Atsushi Kawai, 2003. "A new approximate swaption formula in the LIBOR market model: an asymptotic expansion approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 49-74.
    19. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    20. 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.

    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:wsi:ijtafx:v:21:y:2018:i:04:n:s0219024918500206. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.