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.
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Brace A., Ga̧tarek D. and Musiela M. (1997). The market model of interest rates. Math. Financ. 7: 127–147
Galluccio S., Huang Z., Ly J.-M. and Scaillet O. (2007). Theory and calibration of swap market models. Math. Financ. 17: 111–141
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
Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. North Holland/Kodansha, Amsterdam/Tokyo (1981)
Jamshidian F. (1997). Libor and swap market models and measures. Finance Stoch. 7: 293–330
Jamshidian F. (2006). Bivariate support of forward Libor and swap rates, Working paper. NIBCapital Bank and University of Twente, Netherlands
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
Musiela M. and Rutkowski M. (1997). Continuous-time term structure models: forward measure approach. Finance Stoch. 1: 261–291
Pietersz R. and van Regenmortel M. (2006). Generic market models. Finance Stoch. 10: 507–528
Rogers L.C.G. and Williams D. (2000). Diffusions, Markov Processes and Martingales, vol. 2. Cambridge University Press, Cambridge
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)
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Mataix-Pastor received support from the Instituto Credito Oficial (ICO), Spain, and Fundación Caja Madrid.
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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
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DOI: https://doi.org/10.1007/s00780-006-0032-2