Bivariate support of forward libor and swap rates

F. Jamshidian

    Research output: Contribution to journalArticleAcademic

    2 Citations (Scopus)

    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 < 0 , and explicitly calculate the threshold time at or before which L*t remains positive a.s.
    Original languageEnglish
    Pages (from-to)427-443
    JournalMathematical finance
    Volume18
    Issue number3
    DOIs
    Publication statusPublished - 2008

    Keywords

    • Support
    • swap market model
    • negative Libor
    • IR-72364
    • geometric Brownian motion

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