Skip to main content
Log in

Negative Libor rates in the swap market model

  • Published:
Finance and Stochastics Aims and scope Submit manuscript

Abstract

We apply Stroock and Varadhan’s support theorem to show that there is a positive probability that within the Swap Market Model the implied Libor rates become negative in finite time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Brace A., Ga̧tarek D. and Musiela M. (1997). The market model of interest rates. Math. Financ. 7: 127–147

    Article  MATH  MathSciNet  Google Scholar 

  2. Galluccio S., Huang Z., Ly J.-M. and Scaillet O. (2007). Theory and calibration of swap market models. Math. Financ. 17: 111–141

    Article  Google Scholar 

  3. Galluccio S. and Hunter C. (2004). The co-initial swap market model. Economic Notes by Banca Monte dei Paschi di Siena SpA 33: 209–232

    Google Scholar 

  4. Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. North Holland/Kodansha, Amsterdam/Tokyo (1981)

  5. Jamshidian F. (1997). Libor and swap market models and measures. Finance Stoch. 7: 293–330

    Article  Google Scholar 

  6. Jamshidian F. (2006). Bivariate support of forward Libor and swap rates, Working paper. NIBCapital Bank and University of Twente, Netherlands

    Google Scholar 

  7. Miltersen K., Sandmann K. and Sondermann D. (1997). Closed form solutions for term structure derivatives with log-normal interest rates. J. Finance 52: 409–430

    Article  Google Scholar 

  8. Musiela M. and Rutkowski M. (1997). Continuous-time term structure models: forward measure approach. Finance Stoch. 1: 261–291

    Article  MATH  Google Scholar 

  9. Pietersz R. and van Regenmortel M. (2006). Generic market models. Finance Stoch. 10: 507–528

    Article  Google Scholar 

  10. Rogers L.C.G. and Williams D. (2000). Diffusions, Markov Processes and Martingales, vol. 2. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  11. Stroock, D.W., Varadhan, S.R.S.: On the support of diffusion processes with applications to the strong maximum principle. In: Proceedings of the 6th Berkeley Symposium in Mathematical Statistical Probability, vol. 3, pp. 333–359 (1972)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mark H. A. Davis.

Additional information

Mataix-Pastor received support from the Instituto Credito Oficial (ICO), Spain, and Fundación Caja Madrid.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Davis, M.H.A., Mataix-Pastor, V. Negative Libor rates in the swap market model. Finance Stoch 11, 181–193 (2007). https://doi.org/10.1007/s00780-006-0032-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00780-006-0032-2

Keywords

JEL Classification

Mathematics Subject Classification (2000)

Navigation