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Bivariate Support Of Forward Libor And Swap Rates

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  • Farshid Jamshidian

Abstract

Based on a certain notion of “prolific process,” we find an explicit expression for the bivariate (topological) support of the solution to a particular class of 2 × 2 stochastic differential equations that includes those of the three‐period “lognormal” Libor and swap market models. This yields that in the lognormal swap market model (SMM), the support of the 1 × 1 forward Libor L*t equals [l*t, ∞) for some semi‐explicit −1 ≤l*t≤ 0, sharpening a result of Davis and Mataix‐Pastor (2007) that forward Libor rates (eventually) become negative with positive probability in the lognormal SMM. We classify the instances l*t

Suggested Citation

  • Farshid Jamshidian, 2008. "Bivariate Support Of Forward Libor And Swap Rates," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 427-443, July.
    • Handle: RePEc:bla:mathfi:v:18:y:2008:i:3:p:427-443
    DOI: 10.1111/j.1467-9965.2008.00340.x
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    References listed on IDEAS

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    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Mark Davis & Vicente Mataix-Pastor, 2007. "Negative Libor rates in the swap market model," Finance and Stochastics, Springer, vol. 11(2), pages 181-193, April.
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