IDEAS home Printed from https://ideas.repec.org/a/kap/revdev/v3y1999i2p157-181.html
   My bibliography  Save this article

Stochastic duration and fast coupon bond option pricing in multi-factor models

Author

Listed:
  • Claus Munk

Abstract

Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known models. It is also demonstrated by analytical arguments and numerical examples that the price of a European option on a coupon bond (and, hence, of a European swaption) can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond. Copyright Kluwer Academic Publishers 1999

Suggested Citation

  • 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.
    • Handle: RePEc:kap:revdev:v:3:y:1999:i:2:p:157-181
    DOI: 10.1023/A:1009654427422
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1009654427422
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1009654427422?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. Chen, Ren-Raw & Scott, Louis O, 1992. "Pricing Interest Rate Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure," The Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 613-636.
    2. Gibbons, Michael R & Ramaswamy, Krishna, 1993. "A Test of the Cox, Ingersoll, and Ross Model of the Term Structure," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 619-658.
    3. Longstaff, Francis A., 1993. "The valuation of options on coupon bonds," Journal of Banking & Finance, Elsevier, vol. 17(1), pages 27-42, February.
    4. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    5. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    6. 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.
    7. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    8. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    9. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    10. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
    11. 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. Hansen, Thomas Lyse & Jensen, Bjarne Astrup, 2005. "Energy Options in an HJM Framework," Working Papers 2004-10, Copenhagen Business School, Department of Finance.
    2. 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.
    3. 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.
    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. 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.
    6. Frédéric Godin & Ramin Eghbalzadeh & Patrice Gaillardetz, 2023. "Pricing swaptions and zero-coupon futures options under the discrete-time arbitrage-free Nelson–Siegel model," Review of Derivatives Research, Springer, vol. 26(2), pages 171-206, October.
    7. Joel R. Barber, 2005. "Bond Option Valuation for Non‐Markovian Interest Rate Processes," The Financial Review, Eastern Finance Association, vol. 40(4), pages 519-532, November.
    8. Patrick Büchel & Michael Kratochwil & Maximilian Nagl & Daniel Rösch, 2022. "Deep calibration of financial models: turning theory into practice," Review of Derivatives Research, Springer, vol. 25(2), pages 109-136, July.
    9. 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.
    10. James M. O'Brien, 2000. "Estimating the value and interest rate risk of interest-bearing transactions deposits," Finance and Economics Discussion Series 2000-53, Board of Governors of the Federal Reserve System (U.S.).
    11. João Pedro Vidal Nunes & Pedro Miguel Silva Prazeres, 2014. "Pricing Swaptions Under Multifactor Gaussian Hjm Models," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 762-789, October.
    12. Hitesh Doshi & Hyung Joo Kim & Sang Byung Seo, 2023. "Options on Interbank Rates and Implied Disaster Risk," Finance and Economics Discussion Series 2023-054, Board of Governors of the Federal Reserve System (U.S.).
    13. Anders B. Trolle & Eduardo S. Schwartz, 2006. "A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives," NBER Working Papers 12337, National Bureau of Economic Research, Inc.
    14. Luís Oliveira & João Vidal Nunes & Luís Malcato, 2014. "The performance of deterministic and stochastic interest rate risk measures:," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 13(3), pages 141-165, December.
    15. Oh Kwon, 2007. "Duration, factor sensitivities, and interest rate Greeks," Annals of Finance, Springer, vol. 3(4), pages 471-486, October.
    16. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2020. "Valuation of caps and swaptions under a stochastic string model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(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. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    2. repec:uts:finphd:40 is not listed on IDEAS
    3. 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.
    4. Berardi, Andrea, 1995. "Estimating the Cox, ingersoll and Ross model of the term structure: a multivariate approach," Ricerche Economiche, Elsevier, vol. 49(1), pages 51-74, March.
    5. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018, January-A.
    6. Vetzal, Kenneth R., 1997. "Stochastic volatility, movements in short term interest rates, and bond option values," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 169-196, February.
    7. Casassus, Jaime & Collin-Dufresne, Pierre & Goldstein, Bob, 2005. "Unspanned stochastic volatility and fixed income derivatives pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2723-2749, November.
    8. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    9. Ren-Raw Chen & Brian A. Maris & Tyler T. Yang, 1999. "Valuing Fixed-Income Options and Mortgage-Backed Securities with Alternative Term Structure Models," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 26(1-2), pages 33-55.
    10. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Boero, G. & Torricelli, C., 1996. "A comparative evaluation of alternative models of the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 93(1), pages 205-223, August.
    17. repec:wyi:journl:002108 is not listed on IDEAS
    18. repec:dau:papers:123456789/5374 is not listed on IDEAS
    19. Zura Kakushadze, 2015. "Coping with Negative Short-Rates," Papers 1502.06074, arXiv.org, revised Aug 2015.
    20. Jiang, George J., 1997. "A generalized one-factor term structure model and pricing of interest rate derivative securities," Research Report 97A34, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    21. 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.
    22. Jing Yuan & Yan Peng & Zongwu Cai & Zhengyi Zhang, 2021. "A Quantitative Evaluation to Interest Rate Marketization Reform in China," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202122, University of Kansas, Department of Economics.
    23. 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.

    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:kap:revdev:v:3:y:1999:i:2:p:157-181. 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.