IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v16y2019i1d10.1007_s10287-018-0323-z.html
   My bibliography  Save this article

Calibration of one-factor and two-factor Hull–White models using swaptions

Author

Listed:
  • Vincenzo Russo

    (Assicurazioni Generali S.p.A.)

  • Gabriele Torri

    (University of Bergamo
    VŠB-TU Ostrava)

Abstract

In this paper, we analize a novel approach for calibrating the one-factor and the two-factor Hull–White models using swaptions under a market-consistent framework. The technique is based on the pricing formulas for coupon bond options and swaptions proposed by Russo and Fabozzi (J Fixed Income 25:76–82, 2016b; J Fixed Income 27:30–36, 2017b). Under this approach, the volatility of the coupon bond is derived as a function of the stochastic durations. Consequently, the price of coupon bond options and swaptions can be calculated by simply applying standard no-arbitrage pricing theory given the equivalence between the price of a coupon bond option and the price of the corresponding swaption. This approach can be adopted to calibrate parameters of the one-factor and the two-factor Hull–White models using swaptions quoted in the market. It represents an alternative with respect to the existing approaches proposed in the literature and currently used by practitioners. Numerical analyses are provided in order to highlight the quality of the calibration results in comparison with existing models, addressing some computational issues related to the optimization model. In particular, calibration results and sensitivities are provided for the one- and the two-factor models using market data from 2011 to 2016. Finally, an out-of-sample analysis is performed in order to test the ability of the model in fitting swaption prices different from those used in the calibration process.

Suggested Citation

  • Vincenzo Russo & Gabriele Torri, 2019. "Calibration of one-factor and two-factor Hull–White models using swaptions," Computational Management Science, Springer, vol. 16(1), pages 275-295, February.
    • Handle: RePEc:spr:comgts:v:16:y:2019:i:1:d:10.1007_s10287-018-0323-z
    DOI: 10.1007/s10287-018-0323-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-018-0323-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10287-018-0323-z?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. Claus Munk, 1999. "Stochastic duration and fast coupon bond option pricing in multi-factor models," Review of Derivatives Research, Springer, vol. 3(2), pages 157-181, May.
    2. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    4. David F. Schrager & Antoon A. J. Pelsser, 2006. "Pricing Swaptions And Coupon Bond Options In Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 673-694, October.
    5. L. Ingber, 1996. "Adaptive simulated annealing (ASA): Lessons learned," Lester Ingber Papers 96as, Lester Ingber.
    6. F. Jamshidian, 1995. "A simple class of square-root interest-rate models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(1), pages 61-72.
    7. Longstaff, Francis A & Schwartz, Eduardo S, 1992. "Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-1282, September.
    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. Indu Rani & Chandan Kumar Verma, 2024. "Analyzing Short-Rate Models for Efficient Bond Option Pricing: A Review," SN Operations Research Forum, Springer, vol. 5(3), pages 1-26, September.
    2. Claudio Fontana & Francesco Rotondi, 2022. "Valuation of general GMWB annuities in a low interest rate environment," Papers 2208.10183, arXiv.org, revised Aug 2023.
    3. Fontana, Claudio & Rotondi, Francesco, 2023. "Valuation of general GMWB annuities in a low interest rate environment," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 142-167.
    4. Kladívko, Kamil & Rusý, Tomáš, 2023. "Maximum likelihood estimation of the Hull–White model," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 227-247.

    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. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    2. Date, Paresh & Wang, Chieh, 2009. "Linear Gaussian affine term structure models with unobservable factors: Calibration and yield forecasting," European Journal of Operational Research, Elsevier, vol. 195(1), pages 156-166, May.
    3. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.
    4. Rogers, L. C. G. & Stummer, Wolfgang, 2000. "Consistent fitting of one-factor models to interest rate data," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 45-63, August.
    5. Thorsten Moenig, 2021. "Efficient valuation of variable annuity portfolios with dynamic programming," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 1023-1055, December.
    6. repec:uts:finphd:40 is not listed on IDEAS
    7. Oh Kwon, 2009. "On the equivalence of a class of affine term structure models," Annals of Finance, Springer, vol. 5(2), pages 263-279, March.
    8. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    9. Jury Falini, 2009. "Pricing caps with HJM models: the benefits of humped volatility," Department of Economics University of Siena 563, Department of Economics, University of Siena.
    10. 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.
    11. Oldrich Alfons Vasicek & Francisco Venegas-Martínez, 2021. "Models of the Term Structure of Interest Rates: Review, Trends, and Perspectives," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(2), pages 1-28, Abril - J.
    12. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    13. Antonio Díaz & Francisco Jareño & Eliseo Navarro, 2022. "Yield curve data choice and potential moral hazard: An empirical exercise on pricing callable bonds," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(2), pages 2124-2145, April.
    14. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 20, pages 1207-1246, Elsevier.
    15. repec:wyi:journl:002108 is not listed on IDEAS
    16. Alain Monfort & Fulvio Pegoraro, 2006. "Multi-Lag Term Structure Models with Stochastic Risk Premia," Working Papers 2006-29, Center for Research in Economics and Statistics.
    17. Marco Di Francesco & Roberta Simonella, 2023. "A stochastic Asset Liability Management model for life insurance companies," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(1), pages 61-94, March.
    18. de Jong, Frank, 2000. "Time Series and Cross-Section Information in Affine Term-Structure Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 300-314, July.
    19. Shane Miller & Eckhard Platen, 2004. "A Two-Factor Model for Low Interest Rate Regimes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 107-133, March.
    20. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2007, January-A.
    21. repec:dau:papers:123456789/5374 is not listed on IDEAS
    22. Wali Ullah, 2017. "Term structure forecasting in affine framework with time-varying volatility," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 453-483, August.
    23. Zura Kakushadze, 2015. "Coping with Negative Short-Rates," Papers 1502.06074, arXiv.org, revised Aug 2015.

    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:comgts:v:16:y:2019:i:1:d:10.1007_s10287-018-0323-z. 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.