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Stochastic Hyperbolic Dynamics For Infinite‐Dimensional Forward Rates And Option Pricing

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  • Shin Ichi Aihara
  • Arunabha Bagchi

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.

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  • Shin Ichi Aihara & Arunabha Bagchi, 2005. "Stochastic Hyperbolic Dynamics For Infinite‐Dimensional Forward Rates And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 27-47, January.
    • Handle: RePEc:bla:mathfi:v:15:y:2005:i:1:p:27-47
    DOI: 10.1111/j.0960-1627.2005.00209.x
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    Cited by:

    1. M. De Donno & M. Pratelli, 2006. "A theory of stochastic integration for bond markets," Papers math/0602532, arXiv.org.
    2. Micha{l} Barski & Jacek Jakubowski & Jerzy Zabczyk, 2008. "On incompleteness of bond markets with infinite number of random factors," Papers 0809.2270, arXiv.org, revised Jan 2016.
    3. Roncoroni, Andrea & Galluccio, Stefano & Guiotto, Paolo, 2010. "Shape factors and cross-sectional risk," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2320-2340, November.

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