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Valuation of Two-Factor Interest Rate Contingent Claims Using Green's Theorem

  • Ghulam Sorwar
  • Giovanni Barone-Adesi
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    Over the years a number of two-factor interest rate models have been proposed that have formed the basis for the valuation of interest rate contingent claims. This valuation equation often takes the form of a partial differential equation that is solved using the finite difference approach. In the case of two-factor models this has resulted in solving two second-order partial derivatives leading to boundary errors, as well as numerous first-order derivatives. In this article we demonstrate that using Green's theorem, second-order derivatives can be reduced to first-order derivatives that can be easily discretized; consequently, two-factor partial differential equations are easier to discretize than one-factor partial differential equations. We illustrate our approach by applying it to value contingent claims based on the two-factor CIR model. We provide numerical examples that illustrate that our approach shows excellent agreement with analytical prices and the popular Crank-Nicolson method.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.531588
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    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 18 (2011)
    Issue (Month): 4 ()
    Pages: 277-289

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    Handle: RePEc:taf:apmtfi:v:18:y:2011:i:4:p:277-289
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