An infinite factor model for the interest rate derivatives

Arunabha Bagchi, K. Suresh Kumar

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

    Abstract

    In this paper we model the forward rate process as a stochastic partial differential equation in a Sobolev space. We establish the existence of a martingale measure. We also derive the price of a general contigent claim as the solution to a partial differential equation in an appropriate Hilbert space. Moreover we obtain an explicit formula for the price of the interest rate cap in the Gaussian framework.
    Original languageEnglish
    Title of host publicationMathematical Finance
    Subtitle of host publicationWorkshop of the Mathematical Finance Research Project, Konstanz, Germany, October 5–7, 2000
    EditorsMichael Kohlmann, Shanjian Tang
    Place of PublicationBasel
    PublisherBirkhäuser
    Pages59-68
    Number of pages10
    ISBN (Electronic)978-3-0348-8291-0
    ISBN (Print)978-3-0348-9506-4
    DOIs
    Publication statusPublished - 2001
    EventWorkshop of the Mathematical Finance Research Project 2000 - Konstanz, Germany
    Duration: 5 Oct 20007 Oct 2000

    Publication series

    NameTrends in Mathematics
    PublisherBirkhäuser

    Workshop

    WorkshopWorkshop of the Mathematical Finance Research Project 2000
    CountryGermany
    CityKonstanz
    Period5/10/007/10/00

    Keywords

    • Interest rate
    • Forward rate
    • Martingale measure
    • Stochastic partial differential equations
    • Gaussian random field

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  • Cite this

    Bagchi, A., & Suresh Kumar, K. (2001). An infinite factor model for the interest rate derivatives. In M. Kohlmann, & S. Tang (Eds.), Mathematical Finance: Workshop of the Mathematical Finance Research Project, Konstanz, Germany, October 5–7, 2000 (pp. 59-68). (Trends in Mathematics). Basel: Birkhäuser. https://doi.org/10.1007/978-3-0348-8291-0_5