Stochastic hyperbolic dynamics for infinite-dimensional forward rates and option pricing

Shin Ichi Aihara, Arunabha Bagchi*

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    17 Citations (Scopus)

    Abstract

    We model the term-structure modeling of interest rates by considering the forward rate as the solution of a stochastic hyperbolic partial differential equation. First, we study the arbitrage-free model of the term structure and explore the completeness of the market. We then derive results for the pricing of general contingent claims. Finally we obtain an explicit formula for a forward rate cap in the Gaussian framework from the general results.
    Original languageEnglish
    Pages (from-to)27-47
    Number of pages20
    JournalMathematical finance
    Volume15
    Issue number1
    DOIs
    Publication statusPublished - 2005

    Keywords

    • European options
    • Stochastic hyperbolic systems
    • Option pricing
    • Completeness

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